Test: MCQs (One or More Correct Option): Vector Algebra and Three Dimensional Geometry | JEE Advanced - JEE MCQ

The vector 

If    and  are linearly dependent vectors and 

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

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?

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?