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

71. For given vectors,

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

find the unit vector in the direction of the vector

straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top

77 Views

72.

If $straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top$ , $straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top$ and $straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top$ , find a vector parallel to the vector $2 space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 space straight c with rightwards arrow on top$ .

73 Views

73. Find a vector in the direction of vector $5 space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top$ which has magnitude 8 units.

Let $straight a with rightwards arrow on top space equals space 5 straight i with hat on top space minus space straight j with hat on top space plus space 2 straight k with hat on top$
$therefore space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 5 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 25 plus 1 plus 4 end root space equals space square root of 30$
Unit vector along $straight a with rightwards arrow on top$ is
$equals space fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator 1 over denominator square root of 30 end fraction left parenthesis 5 straight i with hat on top space minus space straight j with hat on top space plus space 2 straight k with hat on top right parenthesis$
Required vector = $8 space open parentheses fraction numerator straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction close parentheses space equals space fraction numerator 8 over denominator square root of 30 end fraction left parenthesis 5 space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis$
$equals space fraction numerator 40 over denominator square root of 30 end fraction straight i with hat on top space minus space fraction numerator 8 over denominator square root of 30 end fraction straight j with hat on top space plus space fraction numerator 16 over denominator square root of 30 end fraction straight k with hat on top$