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

261. Find the area of the parallelogram whose adjacent sides are determined by the vectors

straight a with rightwards arrow on top space equals straight i with hat on top space minus straight j with hat on top plus 3 space straight k with hat on top

and

straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 7 space straight j with hat on top space plus space straight k with hat on top.

73 Views

262. Find the area of the parallelogram determined by the vectors

3 space straight i with hat on top space plus space 4 space straight j with hat on top space and 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.

74 Views

263. Find the area of a parallelogram whose adjacent sides are given by the vectors

straight a with rightwards arrow on top space equals 3 straight i with hat on top space plus straight j with hat on top space plus space 4 space straight k with hat on top

and

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

72 Views

264. Determine the area of the parallelogram, whose adjacent sides are given by the vectors
$straight i with hat on top minus straight j with hat on top minus straight k with hat on top space and space space 3 space straight i with hat on top space plus space 4 space straight j with hat on top space minus space 5 space straight k with hat on top.$

Let $straight a with rightwards arrow on top space equals space straight i with hat on top space minus space straight j with hat on top space minus space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 4 space straight j with hat on top space minus space 5 space straight k with hat on top$
$straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell space space space straight j with hat on top end cell cell straight k with hat on top end cell row 1 cell negative 1 end cell cell negative 1 end cell row 3 cell space space 4 end cell cell negative 5 end cell end table close vertical bar$
$equals straight i with hat on top space open vertical bar table row cell negative 1 end cell cell negative 1 end cell row 4 cell negative 5 end cell end table close vertical bar space minus space straight j with hat on top space open vertical bar table row 1 cell negative 1 end cell row 3 cell negative 5 end cell end table close vertical bar space plus straight k with hat on top space open vertical bar table row 1 cell negative 1 end cell row 3 4 end table close vertical bar equals space left parenthesis 5 plus 4 right parenthesis space straight i with hat on top space minus space left parenthesis negative 5 plus 3 right parenthesis space straight j with hat on top space plus space left parenthesis 4 plus 3 right parenthesis space straight k with hat on top space equals space 9 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 7 space straight k with hat on top$
$open vertical bar straight a with rightwards arrow on top space cross times straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 9 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 7 right parenthesis squared end root space equals space square root of 81 plus 4 plus 49 end root space equals space square root of 134$
$therefore space space space area space of space parallelogram space equals space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of 134 space sq. space units.$