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

51. Find the sum of the vectors

straight a 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 straight k with hat on top comma space space straight b with rightwards arrow on top space equals space minus 2 straight i with hat on top space plus space 4 straight j with hat on top space plus space 5 straight k with hat on top comma space straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 6 straight j with hat on top space minus space 7 straight k with hat on top

82 Views

52. Compute the magnitude of the following vectors:

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 space space semicolon space space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space minus space 7 straight j with hat on top space minus space 3 straight k with hat on top semicolon space space straight c with rightwards arrow on top space equals space fraction numerator 1 over denominator square root of 3 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 3 end fraction straight j with hat on top space minus space fraction numerator 1 over denominator square root of 3 end fraction straight k with hat on top

108 Views

53. Write two different vectors having same magnitude.

89 Views

54. Write two different vector having same direction.

88 Views

55. Find the values of x, y and z so that the vectors $straight a with rightwards arrow on top space equals straight x space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight z space straight k with hat on top$ and $straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight y space straight j with hat on top space plus space straight k with hat on top$ are equal.

Here, $straight a with rightwards arrow on top space equals straight x space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight z space straight k with hat on top$ and $straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight y space straight j with hat on top space plus space straight k with hat on top$
We know that two vectors are equal if and only if their corresponding components are equal
$therefore space space space space straight a with rightwards arrow on top space equals space straight b with rightwards arrow on top space space space space space space rightwards double arrow space space space space space space straight x space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight z space straight k with hat on top space equals space 2 space straight i with hat on top space plus space straight y space straight j with hat on top space plus space straight k with hat on top rightwards double arrow space space space space space straight x space equals space 2 comma space space space straight y space equals space 2 comma space space straight z space equals space 1$