Vector Algebra questions
907 published questions with worked solutions.
- Let a , b , c be three non-coplanar vectors and p , q , r are vectors defined by the relations p = b c [ a , b , c ] , q = c a [...
- Let the vectors a , b , c be such that | a |=2, | b |=4 and | c |=4. If the projection of b on a is equal to the projection of c...
- 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...
- The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8 i -6 j and 3 i +4 j -12 k , is
- If | |= 27 , | b |=7 and | b |=35 then b is equal to
- If a = i - 2 j + 3 k and b = 2 i + 3 j - k , then the angle between the vectors (2 a + b ) and ( a + 2 b ) is
- If a , b , c are non-coplaner vectors and p = b c [ a , b , c ] , q = c a [ a , b , c ] , r = a b [ a , b , c ] , then 2 a p + b...
- The Cartesian equation of a line is 2x - 2 = 3y + 1 = 6z - 2, then the vector equation of the line is
- Let a, b and c three vectors having magnitude 1, 1 and 2 respectively. If a ( a c)+ b= 0, then the acute angle between a and c is
- Let the vectors a, b, c and d be such that ( a b) ( c d)= 0. Let P_1 and P_2 be planes determined by the pair of vectors a, b and...
- The number of distinct real values of for which the vectors - ^2 i+ j+ k, i+ ^2 j+ k and, i+ j- ^2 k are coplanar, is
- The value of a for which the volume of parallelepiped formed by i+a j+ k, j+a k and a i+ k becomes minimum is
- Let p and q be the position vectors of P and Q respectively, with respect to O and | p|=p, | q|=q. The points R and S divide PQ...
- If | a|= 26 , | b|=7 and | a b|=35, then a b=
- A vector with magnitude of 3 units, which is perpendicular to each of the vectors a=3 i+ j-4 k and b=6 i+5 j-2 k, is given by
- The vector equation of plane containing the point (1,-1,2) and perpendicular to planes 2x+3y-2z=5 and x+2y-3z=8 is
- The volume of the tetrahedron having vertices (1,-6,10),(-1,-3,7),(5,-1, ) and (7,-4,7) is 11 cu. units, then =
- If | a|=3, | b|=5 and | c|=7 and a+ b+ c= 0, then the angle between a and b is
- If a= i+ j+ k, b= i- j+2 k, c=x i+(x-2) j- k and c linear combination of a and b, then x has the value
- If AB =(2 i+3 j- k) and A(1, 2, -1) is the given point, then the co-ordinates of B are
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