Vector Algebra questions
907 published questions with worked solutions.
- Let x be a vector in the plane containing vectors a =2 i - j + k and b = i +2 j + k . If the vector x is perpendicular to (3 i +2...
- Let a =2 i -3 j +4 k and b =7 i + j -6 k If r a = r b , r .( i +2 j + k )=-3, then r .(2 i -3 j + k ) is equal to :
- A plane passes through the point (0, 0, 0) and perpendicular to the vector i +2 j +3 k ... The equation of the plane containing...
- If a = i + j +3 k , b =- i - j - k and c = i -2 j - k such that a . b =1 and b . c =-3, then 1 3 (( a b ). c ) is equal to ——
- Let c , a , b be a triangle with | a |=8, | b |=7, | c |=10. Projection of vector c on b is equal to :
- Let a and b be two non-zero vector perpendicular to each other and | a |=| b |. If | a b |=| a |, then the angle between the...
- In a triangle ABC, if | BC |=3, | CA |=5 and | BA |=7, then the projection of the vector BA on BC is equal to-
- Let a =2 i + j -2 k and b = i + j . If c is a vector such that a c =| c |, | c - a |=2 2 and the angle between ( a b ) and c is 6...
- Let a , b , c be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle , with the vector a...
- If the shortest distance between the lines r_1 = i +2 j +2 k + ( i -2 j +2 k ), R, >0 and r_2 =-4 i - k + (3 i -2 j -2 k ), R is...
- Let a vector a be coplanar with vectors b =2 i + j + k and c = i - j + k . If a is perpendicular to d =3 i +2 j +6 k , and | a |=...
- Let three vectors a , b and c be such that a b = c , b c = a and | a |=2. Then which one of the following is not true ?
- If the shortest distance between the straight lines 3(x – 1) = 6(y – 2) = 2 (z – 1) and 4(x – 2) = 2(y – ) = (z – 3), R is 1 38 ,...
- The vector equation of the plane passing through the intersection of the planes r ( i + j + k )=1 and r ( i -2 j )=-2, and the...
- Let be an integer. If the shortest distance between the lines x – =2y – 1 = –2z and x = y + 2 = z – is 7 2 2 , then the value of...
- Let three vectors a , b and c be such that c is coplanar with a and b , a c =7 and b is perpendicular to c , where a =- i + j + k...
- Let a = i + j +2 k and b =- i +2 j +3 k . Then the vector product ( a + b ) (( a ( a - b )) b ) is equal to :
- Let a = i + j + k , b and c = j - k be three vectors such that a b = c and a . b =1. If the length of projection vector of the...
- Let a , b , c be vectors such that a = b ( b c ). If magnitudes of the vectors a , b and c are 2,1 and 2 respectively and the...
- Let a =(1,- , ), b =(3, ,- ) and c =(- ,-2,1); , I be three vectors such that a =( b c ). If magnitudes of the vectors a , b and...
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