- If^ are the angles which a line
makes with positive x, y, z axes
respectively, what is the value of cos α
- cos β + cos γ?
(a) 1 (b) -1 (c) 2 (d) 3
- Given, the sphere
and the two
points A(1, -1, 2) and B(2, -3, 4). Which
one of the following is correct?
(a) A, B are inside the sphere (b) A, B
are outside the sphere (c) A is inside
the sphere and B is outside the sphere
(d) A is outside the sphere and B is
inside the sphere - For what value of k are the lines
and
perpendicular to each other?
(a) -2 (b) -1 (c)1 (d) 2
- What is the sum of direction
cosines of a line which is equally
inclined to the positive directions of the
axes?
(a) 3 (b) 1 (c) √ (d) 3/√- What is the angle between the line
6x = 4y = 3z and the plane 3x + 2y – 3z=
4?
(a) 0 (b) π/6 (c) π/3 (d) π/2 - A line makes 45 with positive x-
axis and makes equal angles with
positive y, z axes, respectively. What is
the sum of the three angles which the
line makes with positive x, y and z axes?
(a) 180 (b) 165 (c) 150 (d) 135 - If the centre of the sphere
is (1/2, -1, -1/2), what is the value of
b?
(a) 1 (b) -1 (c) 2 (d) - 2- What is the length of the
perpendicular from the origin to the
plane ax + by + √ z= 1?
(a) 1/(ab) (b) 1/(a + b) (c) a + b (d)
ab
VECTOR ALGEBRA
- Projection of 2 ̂ ̂ ̂ along
̂ ̂ ̂ is:
(a) 2/√ (b) 1/√ (c) √ (d) 2√
- Area of parallelogram ABCD, when
⃗⃗⃗⃗⃗^ = ̂ ̂ ̂ and ⃗⃗⃗⃗⃗⃗^ ̂ ̂is:
(a) 1 sq unit (b) 6 sq units (c) 3 sq
units
(d) none of these
- Area of parallelogram ABCD, when
⃗⃗⃗⃗⃗^ = ̂ ̂ ̂ and ⃗⃗⃗⃗⃗⃗^ ̂ ̂ + ̂ is:
(a) √ sq units (b) 2√ sq units (c)
√^
sq units (d) none of these^ - ̂ ( ̂) ̂ ( ̂) ̂ (
̂) is always equal to:
(a) (b) - (c) 2 (d) - 2