Vector Algebra questions
907 published questions with worked solutions.
- a, b, c are three vectors of which every pair is noncollinear. If the vectors a + b and b + c are collinear with c and a...
- If r = 3 i + 2 j - 5 k, a = 2 i - j + k, b = i + 3 j - 2 k and c = -2 i + j - 3 k such that r = a + b + c then
- The position vectors of three points are 2 a - b + 3 c, a - 2 b + c and a - 5 b where a, b, c are noncoplanar vectors. The points...
- If a = i + j + k, b = 4 i + 3 j + 4 k and c = i + j + k are linearly dependent vectors and | c| = 3 then
- Let OA = a and OB = b. A vector along one of the bisectors of the angle AOB is
- Let | a| = | b| = | a - b| = 1. Then the angle between a and b is
- If a + b = 2 i and 2 a - b = i - j then the angle between a and b is
- Let | a| = 1, | b| = 2, | c| = 3, and a ( b + c), b ( c + a) and c ( a + b). Then | a + b + c| is
- ( a i) i + ( a j) j + ( a k) k is equal to
- If a, b are unit vectors such that a + b is also a unit vector then the angle between the vectors a and b is
- If a i = a ( i + j) = a ( i + j + k) = 1 then a is
- ( a i)^2 + ( a j)^2 + ( a k)^2 is equal to
- | a + b|^2 - | a - b|^2 is equal to
- If a, b, c are the pth, qth, rth terms of an HP and u = (q - r) i + (r - p) j + (p - q) k, v = i a + j b + k c then
- If a + b a and | b| = 2 ,| a| then
- Let = a ( b + c), = b ( c + a) and = c ( a + b). Then
- Let a, b, c be three unit vectors such that | a + b + c| = 1 and a b. If c makes angles , with a, b respectively then + is equal...
- If a, b, c are three vectors of equal magnitude and the angle between each pair of vectors is 3 such that | a + b + c| = 6 then |...
- If | a| = 5, | a - b| = 8 and | a + b| = 10 then | b| is
- If a and b are unit vectors and is the angle between them then 2 is equal to
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