Test: MCQs (One or More Correct Option): Vector Algebra and Three Dimensional Geometry | JEE Advanced - JEE MCQ
20 Questions MCQ Test - Test: MCQs (One or More Correct Option): Vector Algebra and Three Dimensional Geometry | JEE Advanced
and 
be three non-zero vectors such that 
is a unit vector perpendicular to both the vectors 
and 
If the angle between 
then
and be three non-zero vectors such that is a unit vector perpendicular to both the vectors and If the angle between then
The number of vectors of unit length perpendicular to vectors 
then
represent two vectors in opp. directions. 
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Let 
be three vectors. A vector in the plane of 
whose projection on 
be three vectors. A vector in the plane of whose projection on 
The vector 
If 
and 
are linearly dependent vectors and 
and 
are linearly dependent,
for some scalars l and m not all zeros.
For three vectors u, v, w which of the following expression is not equal to any of the remaining three?
Which of the following expressions are meaningful?
Let a and b be two non-collinear unit vectors. If u = a – (a . b) b and v = a × b, then | v | is
Let 
be vector parallel to line of intersection of planes P1 and P2. Plane P1 is parallel to the vectors 
and that P2 is parallel to 
then the angle between vector 
and a given vector 
is given by
The vector (s) which is/are coplanar with vectors 
and 
and perpendicular to the vector 
is/are
If the straight lines 
are coplanar, then the plane (s) containing these two lines is (are)
A line l passing through the origin is perpendicular to the lines
Then, the coordinate(s) of the point(s) on l2 at a distance of 
from the point of intersection of l and l1 is (are)
Two lines 
are coplanar. Then a can take value(s)
Let 
be three vectors each of magnitude 
and the angle between each pair of them is 
is a non-zero vector perpendicular to 
is a non-zero vector perpendicular to 
From a point P(λ, λ, λ), perpendicular PQ and PR are drawn respectively on the lines y = x, z = 1 and y = – x, z = – 1. If P is such that ∠QPR is a right angle, then the possible value(s) of ∠ is/(are)
In R3, consider the planes P1 : y = 0 and P2 : x + z = 1. Let P3 be the plane, different from P1 and P2, which passes through the intersection of P1 and P2. If the distance of the point (0, 1, 0) from P3 is 1 and the distance of a point (α, β, γ) from P3 is 2, then which of the following relations is (are) true?
In R3, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P1 : x + 2y – z + 1 = 0 and P2 : 2x – y + z – 1 = 0. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P1. Which of the following points lie (s) on M?
and 
satisfy the above eqn.Let ΔPQR be a triangle. 
then which of the following is (are) true?
Consider a pyramid OPQRS located in the first octant (x > 0, y > 0, z > 0) with O as origin, and OP and OR along the x–axis and the y–axis, respectively. The base OPQR of the pyramid is a square with OP = 3. The point S is directly above the mid-point, T of diagonal OQ such that TS = 3. Then
Let
be a unit vector in R3 and 
Given that there exists a vector 
in 
Which of the following statement(s) is (are) correct?
is perpendicular to the plane containing 
is perpendicular to 
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