Vector Algebra questions
907 published questions with worked solutions.
- If | a + b| = | a - b| then
- Two vectors a = i + j 3 and b = i 3 + j are
- If a = i + j, b = 2 j - k and r a = b a, r b = a b then r | r| is equal to
- If p, q are two noncollinear and nonzero vectors such that (b - c) , p q + (c - a) , p + (a - b) , q = 0, where a, b, c are the...
- If a, b, c are any three vectors such that ( a + b) c = ( a - b) c = 0 then ( a b) c is
- The unit vector perpendicular to both the vectors a = i + j + k and b = 2 i - j + 3 k and making an acute angle with the vector k...
- Let a = i - 2 j + 3 k , b = 2 i + 3 j - k and c = i + j + (2 - 1) k . If c is parallel to the plane of the vectors a and b then is
- Let a be a unit vector perpendicular to unit vectors b and c and if the angle between b and c be then b c is
- If a b = 0 and a b = 0 then
- The area of the parallelogram whose diagonals represent the vectors 3 i + j - 2 k and i - 3 j + 4 k is
- ( r i )( r i ) + ( r j )( r j ) + ( r k )( r k ) is equal to
- Let a = i + j + k , c = j - k . If b is a vector satisfying a b = c and a b = 3 then b is
- A unit vector perpendicular to the plane passing through the points whose position vectors are i - j + 2 k , 2 i - k and 2 j + k...
- Let r a = b a and r c = 0, where a b 0. Then r is equal to
- For three vectors u , v , w which of the following expressions is not equal to any one of the remaining three options?
- For three noncoplanar vectors a , b , c the relation | a b c | = | a | ,| b | ,| c | holds if and only if
- Let a , b , c be three unit vectors and a b = a c = 0. If the angle between b and c is 3 then |[ a b c ]| is equal to
- Let a, b, c be three distinct positive real numbers. If p , q , r lie in a plane, where p = a i - a j + b k , q = i + k and r = c...
- Which of the following is not equal to [ a b c ]?
- If [ a b c ] = 1 then a b c c a b + b c a a b c + c a b b c a is equal to
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