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

91. Write the direction ratio’s of the vector

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 2 space straight k with hat on top

and hence calculate its direction cosines.

82 Views

92. Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction.

76 Views

93.

If $straight P with rightwards arrow on top left parenthesis 1 comma space 5 comma space 4 right parenthesis$ and $straight Q with rightwards arrow on top space left parenthesis 4 comma space 1 comma space minus 2 right parenthesis$ , find the direction ratios of $PQ with rightwards arrow on top.$

80 Views

Long Answer Type

94. If A (2, – 1, 3), B (8, 5, – 6) and C (4, 1, 0) are the vertices of a triangle. show that
(i) AB = 3 AC
(ii) The direction-cosines of

BC with rightwards arrow on top

are

fraction numerator negative 2 over denominator square root of 17 end fraction comma space fraction numerator negative 2 over denominator square root of 17 end fraction comma space fraction numerator 3 over denominator square root of 17 end fraction.

74 Views

Short Answer Type

95. Show that vector

straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top

is equally inclined to the axes OX. OY and OZ.

77 Views

Long Answer Type

96. Show that the points A (6. – 7, 0) B (16, – 19, – 4). C (0, 3, – 6), D (2, – 5, 10) are such that AB and CD intersect at the point P (1, – 1, 2).

77 Views

97. The vectors of magnitude a, 2a, 3a meet at a point and their directions arc. along the diagonals of three adjacent faces of a cube. Determine the magnitude of their resultant.

263 Views

Short Answer Type

98. Write all the unit vectors in XY-plane.

Let $straight r with rightwards arrow on top space equals space straight x space straight i with hat on top space plus space space straight y space straight j with hat on top space$ be a unit vector $OP with rightwards arrow on top$ in XY - plane.
$therefore space space space space space space OP space equals open vertical bar straight r with rightwards arrow on top close vertical bar space equals space 1 straight P space is space left parenthesis straight x comma space straight y right parenthesis$
From P draw $PM space perpendicular space OX.$
In rt. angled $increment OMP comma$
$straight x over 1 space equals space cos space straight theta comma space space space straight y over 1 space equals space sin space straight theta$

$therefore space straight x space equals space cos space straight theta comma space space space straight y space equals space sin space straight theta therefore space space straight r with rightwards arrow on top space equals space left parenthesis cos space straight theta right parenthesis space straight i with hat on top space plus space left parenthesis sin space straight theta right parenthesis space straight j with hat on top space space space... left parenthesis 1 right parenthesis Here space open vertical bar straight r with rightwards arrow on top close vertical bar space equals space square root of cos squared straight theta plus space sin squared straight theta end root space equals square root of 1 space equals space 1$
Also, as $straight theta$ varies from 0 to $straight pi$ , the point P traces the circle r² + y² = 1 counterclockwise, and this covers all possible directions.
∴ (1) gives every unit vector in the XY-plane.

149 Views

99. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

91 Views

Long Answer Type

100. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

126 Views