Vector Algebra questions
907 published questions with worked solutions.
- Let a = i -2 j + k and b = i - j + k be two vectors. If c is a vector such that b c = b a and c a =0, then c b is equal to :
- Let the position vectors of points 'A' and 'B' be i + j + k and 2 i + j +3 k , respectively. A point 'P' divides the line segment...
- Let a = 6 i + j - k and b = i + j. If c is a vector such that | c| ≥ 6, a c = 6| c|, | c - a| = 2√2 and the angle between a b and...
- Let a = 2 i + j - k, b = (( a ( i + j)) i) i. Then the square of the projection of a on b is:
- If the shortest distance between the lines x - 3 = y - 2 -1 = z - 1 1 and x + 2 -3 = y + 5 2 = z - 4 4 is 44 30 , then the...
- Let a , b and c be three unit vectors such that | a - b |^2+| a - c |^2=8. Then | a +2 b |^2+| a +2 c |^2 is equal to __________.
- The lines r =( i - j )+l(2 i + k ) and r =(2 i - j )+m( i + j - k )
- If the shortest distance between the lines L₁ : r = (2 + λ)î + (1 − 3λ)ĵ + (3 + 4λ)k̂, λ ∈ R, L₂ : r = 2(1 + μ)î + 3(1 + μ)ĵ + (5...
- The set of all α, for which the vector a = t i + 6 j - 3 k and b = t i - 2 j - 2 t k are inclined at an obtuse angle for all t ∈...
- Let a = 9 i - 13 j + 25 k, b = 3 i + 7 j - 13 k and c = 17 i - 2 j + k be three given vectors. If r is a vector such that r a = (...
- Let a = i + 2 j + 3 k, b = 2 i + 3 j - 5 k and c = 3 i - j + k be three vectors. Let r be a unit vector along b + c. If r a = 3,...
- If the shortest distance between the lines x - 2 = y - 4 3 = z - 3 4 and x - 2 4 = y - 4 6 = z - 7 8 is 13 29 , then a value of λ...
- Let a = 4 i - j + k, b = 11 i - j + k and c be a vector such that ( a + b) c = c (-2 a + 3 b). If (2 a + 3 b) c = 1670, then |...
- Let x_0 be the point of local maxima of f(x)= a ( b c ), where a =x i -2 j +3 k , b =-2 i +x j - k and c =7 i -2 j +x k . Then...
- If a =2 i + j +2 k , then the value of | i ( a i ) |^2+ | j ( a j ) |^2+ | k ( a k ) |^2 is equal to _________.
- If the volume of a parallelopiped, whose coterminus edges are given by the vectors a = i + j +n k , b =2 i +4 j -n k and c = i +n...
- Let the vectors a , b , c be such that | a |=2, | b |=4 and | c |=4. If the projection of b on a is equal to the projection of c...
- The shortest distance between the lines x-1 0 = y+1 -1 = z 1 and x + y + z + 1 = 0, 2x – y + z + 3 = 0 is -
- If a and b are unit vectors, then the greatest value of 3 | a + b |+| a - b | is ________.
- If x and y be two non-zero vectors such that | x + y |=| x | and 2 x + y is perpendicular to y , then the value of is __________.
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