Vector Algebra questions
907 published questions with worked solutions.
- What is 3 +2 equal to if (2 i +6 j +27 k ) ( i + j + k ) is a null vector?
- For what value of the angle between the vectors a and b is the quantity | a b |+ 3 | a b | maximum?
- Let be the angle between two unit vectors a and b . If a +2 b is perpendicular to 5 a -4 b , then what is + 2 equal to?
- The vectors a , b and c are of the same length. If taken pairwise, they form equal angles. If a = i + j and b = j + k , then what...
- A line makes angles , and with the positive directions of the coordinate axes. If a=( ^2 ) i+( ^2 ) j+( ^2 ) k and b= i+ j+ k,...
- Consider the following statements in respect of a vector d=( a b) c : I. d is coplanar with a and b. II. d is perpendicular to c....
- The position vectors of three points A, B and C are a, b and c respectively such that 3 a-4 b+ c= 0. What is AB:BC equal to?
- The position vectors of three points A, B and C are a, b and c respectively, where c=( ^2 ) a+( ^2 ) b. What is ( a b)+( b c)+( c...
- Let a, b, ( a b) be unit vectors. What is ( a b) equal to?
- Let p = a - b , q = a + b . If | a |=| b |=2 and a b =2, then what is the value of | p q |?
- How many of the following can be a vector perpendicular to both the vectors 2 i - j + k and i + j +3 k ? I. 4 i +5 j -3 k II. -8...
- What is the area of the parallelogram whose sides are represented by the vectors i +2 j +3 k and 2 i + j +2 k ?
- The position vectors of the vertices A, B, C and D of a quadrilateral ABCD are given by 3 i +4 j -2 k , 4 i -4 j -3 k , 2 i -3 j...
- A force F =2 i - j +5 k is applied at the point A(1, 2, 5). If its moment about the point B(-1, -2, 3) is 16 i -6 j +2 k , then...
- Let a , b , c and d be the vectors. Consider the following : I. ( a b ) ( c d ) II. ( a b ) ( c d ) III. ( a b ) ( c d ) IV. ( a...
- The scalar projection of a = i + j -2 k on b =2 i - j - k is 7/3. What is the value of ?
- Let a and b be unit vectors inclined at 30^ . What is the area of the parallelogram whose sides are represented by the vectors a...
- Let a , b and c be unit vectors such that a b = a c =0. If the angle between b and c is /6, then what is a equal to?
- Consider the following statements in respect of a vector c = a + b , where | a |=| b | 0 : 1. c is perpendicular to ( a - b ). 2....
- If a and b are two vectors such that | a + b |=| a - b |=4, then which one of the following is correct?
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