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.

78 Views

74. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 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 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.

81 Views

75. Show that the vectors

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

and

negative 4 space straight i with hat on top space plus space 6 space straight j with hat on top space minus space 8 space straight k with hat on top

are collinear.

91 Views

76. Find the condition that the vectors

straight a with rightwards arrow on top space equals space straight k space straight i with hat on top space plus space straight l space straight j with hat on top space and space straight b with rightwards arrow on top space equals space straight l space straight i with hat on top space plus space straight k space straight j with hat on top comma space space left parenthesis straight k comma space straight l space not equal to 0 right parenthesis space are space parallel

74 Views

Long Answer Type

77. Prove that if

straight u with rightwards arrow on top space equals space straight u subscript 1 space straight i with hat on top space plus space straight u subscript 2 space straight j with hat on top space and space straight v with rightwards arrow on top space equals space straight v subscript 1 space straight i with hat on top space plus space straight v subscript 2 space straight j with hat on top

are non-zero vectors, then they are parallel if and only if u₂v₂ – u₂v₁ = 0.

73 Views

78. Find the condition that the vectors $straight a with rightwards arrow on top space equals space straight k space straight i with hat on top space plus space 3 space straight j with hat on top space and space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space straight k space straight j with hat on top comma space space left parenthesis straight k space not equal to space 0 right parenthesis$ are parallel.

Here,    $straight a with rightwards arrow on top space equals space straight k straight i with hat on top space plus space 3 straight j with hat on top comma space space straight b with rightwards arrow on top space equals space 4 straight i with hat on top space plus space space straight k straight j with hat on top$
Let $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ be parallel..
   $therefore space space$ there exists a non-zero scalar $straight lambda$ such that
$straight a with rightwards arrow on top space equals space straight lambda straight b with rightwards arrow on top$
$therefore space space straight k space straight i with hat on top space plus space 3 space straight j with hat on top space equals space 4 space straight lambda space straight i with hat on top space plus space straight lambda space straight k space straight j with hat on top therefore space space space left parenthesis straight k space minus space 4 space straight lambda right parenthesis space straight i with hat on top space plus space left parenthesis 3 space minus space straight k space straight lambda right parenthesis space straight j with hat on top space equals space 0 with rightwards arrow on top rightwards double arrow space space space space straight k space minus space 4 space straight lambda space equals space 0 comma space space space space 3 space space minus space straight k space straight lambda space equals space 0 rightwards double arrow space space space space space space space space space space space space space straight lambda space equals straight k over 4 comma space space space space straight lambda space equals space 3 over straight k$
Equating values of $straight lambda comma$ we get,
   $straight k over 4 space equals space 3 over straight k space space space or space space space straight k squared space equals space 4 space cross times space 3 space equals space 12$
which is required condition.