Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Vector Algebra

Short Answer Type

241. Find the unit vector perpendicular to the vectors

straight a with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space 3 space straight j with hat on top space minus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 3 space stack straight j space with hat on top space minus space 3 space straight k with hat on top.

73 Views

242. Find the unit vector perpendicular to vectors

3 straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top comma space space space 2 space straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top

74 Views

243. Find the unit vector perpendicular to vectors

4 space straight i with hat on top space plus space straight j with hat on top space space minus space 3 space straight k with hat on top comma space space space space 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top.

73 Views

244. Find a unit vector perpendicular to vectors

3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top comma space space 2 straight i with hat on top space plus straight j with hat on top space plus 3 straight k with hat on top

71 Views

245. Find a unit vector perpendicular to the plane containing the vectors:

straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space minus space 2 straight k with hat on top space space and space straight b with rightwards arrow on top space equals space straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top

73 Views

246. Find a unit vector perpendicular to each of the vector

open parentheses straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses

and

left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis

, where

straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top comma space space space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space plus space space 3 space straight k with hat on top

76 Views

Long Answer Type

247.

Find a unit vector perpendicular to each of the vector $straight a with rightwards arrow on top plus straight b with rightwards arrow on top space and space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top comma$ where $straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space plus space 2 straight k with hat on top$ and $straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 straight j with hat on top space minus space 2 space straight k with hat on top.$

74 Views

Short Answer Type

248. Find the value of λ so that the two vectors

2 straight i with hat on top space plus space 3 straight j with hat on top space minus straight k with hat on top

and

4 straight i with hat on top plus 6 straight j with hat on top plus straight lambda straight k with hat on top

are (i) parallel (ii) perpendicular to each other.

73 Views

Long Answer Type

249.
Find the value of $straight lambda$ so that the two vectors $2 space straight i with hat on top space minus space 4 space straight j with hat on top space plus space straight k with hat on top space space and space 4 space straight i with hat on top space minus space 8 space straight j with hat on top space plus space straight lambda space straight k with hat on top$ are (i) parallel (ii) perpendicular to each other.

Let $straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 4 space straight j with hat on top space plus space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space minus space 8 space straight j with hat on top space plus space straight lambda space straight k with hat on top$
(i) $straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 2 cell negative 4 end cell 1 row 4 cell negative 8 end cell straight lambda end table close vertical bar space equals space straight i with hat on top space open vertical bar table row cell negative 4 end cell 1 row cell negative 8 end cell straight lambda end table close vertical bar space minus straight j with hat on top space open vertical bar table row 2 cell negative 1 end cell row 4 cell space space space straight lambda end cell end table close vertical bar space plus space straight k with hat on top space open vertical bar table row 2 cell negative 4 end cell row 4 cell negative 8 end cell end table close vertical bar$
$equals space left parenthesis negative 4 straight lambda plus 8 right parenthesis space straight i with hat on top space minus space left parenthesis 2 straight lambda minus 4 right parenthesis space straight j with hat on top space plus space straight k with hat on top space left parenthesis negative 16 plus 16 right parenthesis space equals space left parenthesis negative 4 space straight lambda space plus 8 right parenthesis straight i with hat on top minus left parenthesis 2 straight lambda minus 4 right parenthesis straight j with hat on top$
Since $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space are space parallel$
$therefore space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top$
$therefore space space left parenthesis negative 4 space straight lambda space plus space 8 right parenthesis space straight i with hat on top space minus space left parenthesis 2 space straight lambda space minus space 4 right parenthesis space straight j with hat on top space equals space 0 with rightwards arrow on top rightwards double arrow space space space minus 4 straight lambda plus 8 space equals space 0 comma space space space 2 straight lambda minus 4 space equals space 0 space space space space space space rightwards double arrow space space space straight lambda space equals space 2$
(ii) Since $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ are perpendicular
$therefore space space space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0 therefore space space left parenthesis 2 right parenthesis thin space left parenthesis 4 right parenthesis space plus space left parenthesis negative 4 right parenthesis thin space left parenthesis negative 8 right parenthesis space plus space left parenthesis 1 right parenthesis space straight lambda space equals space 0 therefore space space 8 plus 32 plus straight lambda space equals space 0 space space space space space space space space space space space space space space space space space space rightwards double arrow space space space straight lambda space equals space minus 40$

74 Views

250.

Find the value of $straight lambda$ so that the vectors $2 space straight i with hat on top space plus 4 space straight j with hat on top space minus space 2 space straight k with hat on top$ and $3 straight i with hat on top space plus space 6 straight j with hat on top space plus space straight lambda straight k with hat on top space$ are (i) parallel (ii) perpendicular to each other.