Vector Algebra questions
907 published questions with worked solutions.
- If a and b are unit vectors and is the angle between them, then what is ^2 ( 2 ) equal to?
- Two adjacent sides of a parallelogram are 2 i -4 j +5 k and i -2 j -3 k . What is the magnitude of dot product of vectors which...
- If | a b |^2+| a b |^2=144 and | a |=4, then what is | b | equal to?
- If the vectors a =2 i -3 j + k , b = i +2 j -3 k and c = j +p k are coplanar, then what is the value of p?
- If 4 i + j -3 k and p i +q j -2 k are collinear vectors, then what are the possible values of p and q respectively?
- Consider the following statements : 1. Dot product over vector addition is distributive 2. Cross product over vector addition is...
- Let a , b , c be three non-zero vectors such that a b = c . Consider the following statements : 1. a is unique if b and c are...
- PQRS is a parallelogram. If PR = a and QS = b , then what is PQ equal to?
- Let a and b are two unit vectors such that a +2 b and 5 a -4 b are perpendicular. What is the angle between a and b ?
- Let a , b and c be unit vectors lying on the same plane. What is (3 a +2 b ) (5 a -4 c ) ( b +2 c ) equal to?
- What are the values of x for which the angle between the vectors 2x^2 i +3x j + k and i -2 j +x^2 k is obtuse?
- The position vectors of vertices A, B and C of triangle ABC are respectively j + k , 3 i + j +5 k and 3 j +3 k . What is angle C...
- What is the length of projection of the vector i+2 j+3 k on the vector 2 i+3 j-2 k?
- If is the angle between vectors a and b such that a b 0, then which one of the following is correct?
- The vectors 60 i+3 j, 40 i-8 j and i-52 j are collinear if :
- Consider the following in respect of the vectors a=(0, 1, 1) and b=(1, 0, 1) : 1. The number of unit vectors perpendicular to...
- If two sides of a square lie on the lines 2x+y-3=0 and 4x+2y+5=0, then what is the area of the square in square units?
- Let a = i - j + k and b = i +2 j - k . If a ( b a )= i - j + k , then what is the value of + + ?
- For any vector r , what is ( r i )( r i )+( r j )( r j )+( r k )( r k ) equal to?
- Let a and b are two vectors of magnitude 4 inclined at an angle 3 , then what is the angle between a and a - b ?
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