Vector Algebra questions
907 published questions with worked solutions.
- If a = i +4 j +2 k , b =3 i -2 j +7 k , c =2 i - j +4 k , then a vector d which is parallel to vector a b and c d =15, is
- The unit vector perpendicular to each of the vectors a + b and a - b , where a = i + j + k and b =3 i -2 j +5 k is
- If the area of the parallelogram with a and b as two adjacent sides is 16 sq. units, then the area of the parallelogram having 3...
- Let a , b and c be three unit vectors such that a ( b c )= 3 2 ( b + c ) If b is not parallel to c , then the angle between a and...
- If a = 1 10 (3 i + k ) and b = 1 7 (2 i +3 j -6 k ), then the value of (2 a - b ) [ ( a b ) ( a +2 b ) ] is
- Let a , b , and c be three non-zero vectors such that no two of these are collinear. If the vector a +2 b is collinear with c and...
- If a , b , c are non-coplanar unit vectors such that a ( b c )= ( b + c ) 2 , then the angle between a and b is
- The number of unit vectors perpendicular to a =(1,1,0) and b =(0,1,1) is
- If the vectors a = i - j +2 k , b =2 i +4 j + k and c = i + j + k are mutually orthogonal, then ( , )
- Let a , b and c be three non-zero vectors such that no two of them are collinear and ( a b ) c = 1 3 | b || c | a . If ' ' is the...
- If x = b c [ a b c ] , y = c a [ a b c ] and z = a b [ a b c ] where a , b , c are non-coplanar vectors, then value of x ( a + b...
- If the volume of tetrahedron whose vertices are A (1, -6, 10), B (-1, -3, 7), C (5, -1, k) and D (7, -4, 7) is 11 cu. units, then...
- If a and b are two unit vectors such that 5 a +4 b and a -2 b are perpendicular to each other, then the angle between a and b is
- If a = i + j + k , b = i - j + k and c = i - j - k are three vectors then vector r in the plane of a and b , whose projection on...
- The distance between parallel lines x-1 2 = y-2 -2 = z-3 1 and x 2 = y -2 = z 1 is
- The magnitude of the projection of the vector 2 i +3 j + k on the vector perpendicular to the plane containing the vectors i + j...
- The value of a, so that the volume of parallelepiped formed by i +a j + k , j +a k and a i + k becomes minimum is
- Let u , v and w be vectors such that u + v + w = 0 . If | u |=3, | v |=4 and | w |=5, then the value of u v + v w + w u is
- For non-zero vectors a , b , c , | ( a b ) c |=| a || b || c | holds if and only if
- The shortest distance (in units) between the lines x+1 3 = y+2 1 = z+1 2 and r = (2 i - 2 j + 3 k ) + ( i + 2 j ) is
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