Vector Algebra questions
907 published questions with worked solutions.
- a, b, c are 3 vectors, such that a + b + c = 0, | a| = 1, | b| = 2 | a then a b + b c + c a is equal to
- Consider points A, B, C and D with position vectors 7 i - 4 j + 7 k, i - 6 j + 10 k, - i - 3 j + 4 k and 5 i - j + 5 k...
- If u, v and w are three non-coplanar vectors, then ( u + v - w) ( u - v) ( v - w) equals
- Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a + 2 b is collinear with c and b...
- If a, b, c are non-coplanar vectors and is a real number, then the vectors a + 2 b + 3 c, b + 4 c and (2 - 1) c are non-coplanar...
- Let a, b and c be non-zero vectors such that ( a b) c = 1 3 | b|| c| a. If is the acute angle between the vectors b and c, then...
- With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N. If they act at right angles, then...
- Let u, v, w be such that | u| = 1, | v| = 2, | w| = 3. If the projection v along u is equal to that of w along u and v, w are...
- If C is the mid point of AB and P is any point outside AB, then
- If a, b, c are non-coplanar vectors and is a real number then [ ( a + b) ^2 b c ] = [ a b + c b] for
- Let a = i - k, b = x i + j + (1 - x) k and c = y i + x j + (1 + x - y) k. Then [ a, b, c] depends on
- Let a, b and c be distinct non-negative numbers. If the vectors a i + a j + c k, i + k and c i + c j + b k lie in a plane, then c...
- ABC is a triangle, right angled at A. The resultant of the forces acting along AB , AC with magnitudes 1 AB and 1 AC respectively...
- If ( a b) c = a ( b c), where a, b and c are any three vectors such that a b 0, b c 0, then a and c are
- The values of a, for which the points A, B, C with position vectors 2 i - j + k, i - 3 j - 5 k and a i - 3 j + k respectively are...
- If u and v are unit vectors and is the acute angle between them, then 2 u 3 v is a unit vector for
- Let a = i + j + k, b = i - j + 2 k and c = x i + (x - 2) j - k. If the vector c lies in the plane of a and b, then x equals
- The non-zero vectors a, b and c are related by a = 8 b and c = -7 b. Then the angle between a and c is
- If u, v, w are non-coplanar vectors and p, q are real numbers, then the equality [3 u p v p w] - [p v w q u] - [2 w q v q u] = 0...
- Let a = j - k and c = i - j - k. Then vector b satisfying a b + c = 0 and a b = 3 is
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