A unit vector in the XOY-plane that makes an angle 30° with t

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.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

121.

The angle between the curves, y = x and y2 - x = 0 at the point (1, 1) is

  • π2

  • tan-143

  • π3

  • tan-134


122.

If the distance between (2, 3) and (- 5, 2) is equal to the distance between (x, 2) and (1, 3), then the values of x are

  • - 6, 8

  • 6, 8

  • - 8, 6

  • - 7, 7


123.

The vertices of a triangle are A(3, 7), B (3, 4) and C (5, 4). The equation of the bisector of the angle ABC is

  • y = x + 1

  • y = x - 1

  • y = 3x - 5

  • y = x


124.

If the angle between a and c is 25°, the angle between b and c is 65° and a + b = c, then the angle between a and b is

  • 40°

  • 115°

  • 25°

  • 90°


Advertisement
125.

The projection of the vector 2i + aj - k on the vector i - 2j + k is - 56. Then, the value of a is equal to

  • 1

  • 2

  • - 2

  • 3


Advertisement

126.

A unit vector in the XOY-plane that makes an angle 30° with the vector i + j and makes an angle 60° with i - j is

  • 146 + 2i - 6 - 2j

  • 126 - 2i + 6 + 2j

  • 146 - 2i + 6 + 2j

  • 146 + 2i + 6 - 2j


D.

146 + 2i + 6 - 2j

Let a unit vector in XOY-plane is, a^ = aa

a = a1i + a2j, a = a12 + a22Given vectors let b = i + jand c = i - jFrom question; a^ . b = a^ . b cos30°= 1 . 2 . 32  62 a . ba = 62 a1 + a2 = 62a             ...iand a^ . c = a^ . c cos60°              = 1 . 2 . 12 a . ca = 22a                ...iiFrom Eqs. (i) and (ii),2a1 = 6 + 2a2a1 = 146 + 2a a1a = 146 + 2and a2 = 146 - 2a a2a = 146 - 2So, the unit vector isa^ = 1aa1i + a2ja^ = 146 + 2i + 6 - 2j


Advertisement
127.

The angle between the line r = (i + 2j + 3k) + λ(2i + 3j + 4k) and the plane r - (i + j - 2k) = 0 is

  • 60°

  • 30°

  • 90°


128.

The lines r = i + j - k + (3i - j) and r = 4j - k + µ (2i + 3k) intersect at the point

  • (0, 0, 0)

  • (0, 0, 1)

  • (0, - 4, - 1)

  • (4, 0, - 1)


Advertisement
129.

An equation of the plane through the points (1, 0, 0) and (0, 2, 0) and at a distance 67 units from the origin is

  • 6x + 3y + z - 6 = 0

  • 6x + 3y + 2z - 6= 0

  • 6x + 3y + z + 6 = 0

  • 6x + 3y + 2z + 6 = 0


130.

The projection of a line segment on the axes are 9, 12 and 8. Then, the length of the line segment is

  • 15

  • 16

  • 17

  • 18


Advertisement