Vector Algebra questions
907 published questions with worked solutions.
- If a = i - j + k , b =2 i +3 j +2 k and c = i +m j +n k are three coplanar vectors and | c |= 6 , then which one of the following...
- Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin. What is OA + OB + OC + OD equal to?
- If a b = c and b c = a , then which one of the following is correct?
- If a =2 i +3 j +4 k and b =3 i +2 j - k are perpendicular, then what is the value of ?
- Let = i +2 j - k , =2 i - j +3 k and =2 i + j +6 k be three vectors. If and are both perpendicular to the vector and =10, then...
- If a and b are two unit vectors, then the vector ( a + b ) ( a b ) is parallel to
- If the vectors a i + j + k , i +b j + k and i + j +c k (a, b, c 1) are coplanar, then the value of 1 1-a + 1 1-b + 1 1-c is equal...
- If a and b are vectors such that | a |=2, | b |=7 and a b =3 i +2 j +6 k , then what is the acute angle between a and b ?
- Let p and q be the position vectors of the points P and Q respectively with respect to origin O. The points R and S divide PQ...
- What is the moment about the point i +2 j - k of a force represented by 3 i + k acting through the point 2 i - j +3 k ?
- If a +2 b +3 c = 0 and a b + b c + c a = ( b c ), then what is the value of ?
- Let | a | 0, | b | 0. ( a + b ) ( a + b )=| a |^2+| b |^2 holds if and only if
- If r =x i +y j +z k , then what is r ( i + j + k ) equal to?
- A unit vector perpendicular to each of the vectors 2 i - j + k and 3 i -4 j - k is
- If | a |=3, | b |=4 and | a - b |=5, then what is the value of | a + b |?
- What is ( a - b ) ( a + b ) equal to?
- In a triangle ABC, if taken in order, consider the following statements : 1. AB + BC + CA = 0 2. AB + BC - CA = 0 3. AB - BC + CA...
- What is the scalar projection of a = i -2 j + k on b =4 i -4 j +7 k ?
- Consider the following equations for two vectors a and b : 1. ( a + b ) ( a - b )=| a |^2-| b |^2 2. (| a + b | ) (| a - b | )=|...
- Consider the following statements : 1. The magnitude of a b is same as the area of a triangle with sides a and b 2. If a b = 0...
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