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
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Let be three vectors. A vector in the plane of
whose projection on
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?
327 docs|185 tests
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327 docs|185 tests
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