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

Long Answer Type

231.

Prove, using vectors, that the altitudes of a triangle are concurrent.
OR
Prove that the perpendicular from the vertices to the opposite sides of a triangle are concurrent.

141 Views

232. Show that the diagonals of a rhombus bisect each other at right angles.

84 Views

233. In a triangle OAB , ∠AOB = 90°. If P and Q are the points of trisection of AB, prove that

OP squared space plus space OQ squared space equals space 5 over 9 AB squared

92 Views

234. In a tetrahedron, if two pairs of opposite edges are perpendicular, then the third pair is also perpendicular to each other and the sum of the sequares of two opposite edges is the same for each pair.

93 Views

235.

Find $straight lambda space and space straight mu$ if $left parenthesis 2 space straight i with hat on top space plus space 6 space straight j with hat on top space plus space 27 space straight k with hat on top right parenthesis space cross times left parenthesis straight i with hat on top space cross times space straight lambda space straight j with hat on top space plus space straight mu space straight k with hat on top right parenthesis space equals space 0 with rightwards arrow on top.$

74 Views

Short Answer Type

236.

Find $open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar comma space space space if space space straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus straight j with hat on top space plus space 3 straight k with hat on top space and space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 2 space straight k with hat on top.$

77 Views

237.

Find $open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar$ if $straight a with rightwards arrow on top space equals straight i with hat on top space minus space 7 space straight j with hat on top space plus space 7 space straight k with hat on top$ and $straight b with rightwards arrow on top space equals space 3 straight i with hat on top space minus space 2 straight j with hat on top space plus space 2 straight k with hat on top$

73 Views

238.

If $straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top space and space straight b with rightwards arrow on top space equals 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top comma space space find space open vertical bar 2 straight b with rightwards arrow on top cross times space straight a with rightwards arrow on top close vertical bar.$

76 Views

Long Answer Type

239.

If $straight a with rightwards arrow on top space equals straight i with hat on top space minus straight j with hat on top space plus space 2 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 3 space straight j with hat on top space minus space 4 space straight k with hat on top comma$ then show that $straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space minus straight b with rightwards arrow on top space cross times space straight a with rightwards arrow on top$

73 Views

Short Answer Type

240. Find a unit vector perpendicular to both $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ if $straight a with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 2 space straight k with hat on top space space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 3 space straight k with hat on top$

Here, $straight a with rightwards arrow on top space equals 4 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 2 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 5 space straight j with hat on top space minus space 3 space straight k with hat on top$
$therefore space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 4 3 2 row 2 5 cell negative 3 end cell end table close vertical bar space equals space left parenthesis negative 9 minus 10 right parenthesis space straight i with hat on top space minus space left parenthesis negative 12 minus 4 right parenthesis straight j with hat on top space plus space left parenthesis 20 minus 6 right parenthesis space straight k with hat on top space space space space equals space minus 19 space straight i with hat on top space plus space 16 space straight j with hat on top space plus 14 space straight k with hat on top$
which is a vector perpendicular to both $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.$
$open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals square root of left parenthesis negative 19 right parenthesis squared plus left parenthesis 16 right parenthesis squared plus left parenthesis 14 right parenthesis squared end root space equals square root of 361 plus 256 plus 196 end root space equals square root of 813$
$therefore space space space$ a unit vector perpendicular to $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space equals space fraction numerator straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar end fraction$
$equals space fraction numerator 1 over denominator square root of 813 end fraction left parenthesis negative 19 space straight i with hat on top space plus space 16 space straight j with hat on top space plus space 14 space straight k with hat on top right parenthesis$

73 Views

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

Short Answer Type

Long Answer Type

Short Answer Type

240. Find a unit vector perpendicular to both if