Vector Algebra questions
907 published questions with worked solutions.
- The unit vector which is orthogonal to the vector 3 i + 2 j + 6 k and coplanar with the vectors 2 i + j + k and i + j + k is
- If a , b , c are three non-zero vectors, no two of them are collinear, a + 2 b is collinear with c , b + 3 c is collinear with a...
- If the volume of tetrahedron, whose vertices are A(1, 2, 3), B (-3, -1, 1), C(2, 1, 3) and D(-1, 2, x) is 11 6 cubic units, then...
- If a , b , c are three vectors, | a |=2, | b |=4, | c |=1, | b c |= 15 and b =2 c + a , then the value of is
- Let A be a vector parallel to line of intersection of planes P_1 and P_2 through origin. P_1 is parallel to the vectors 2 j +3 k...
- If a , b , c are three non zero and non-coplanar vectors such that a ( b c )= b 2 , then the angle between a and b is …………
- If a , b and c are non-coplanar unit vectors such that the angle between any two of them is 60^o, and the vector d =x a +y b +z c...
- If a = i + j + k , b = i , c =c_1 i +c_2 j +c_3 k with c_1=1,c_2=2, then value of c_3 such that a , b , c are coplanar is _____
- If a and b have the same magnitude and angle between them is 60^o and their scalar product is 12, then | a | is _____
- If a = i + j and b = i - k , then the point of intersection of the lines r a = b a and r b = a b is
- The equation of a line passing through a point (4,-2,3) and perpendicular to the XZ-plane is …..
- The vector equation of the plane which is at a distance of 5 units from the origin and normal to the vector 2 i + j -2 k is
- If a parallelogram is constructed on the vectors a =3 p - q , b = p +3 q and | p |=3, | q |=2 and angle between p and q is 3,...
- Let a, b, c be unit vectors such that a is perpendicular to the plane of b and c. If the angle between b and c is 3, then | a+ b+...
- The volume of a tetrahedron with vertices 5 i- j+ k, 7 i-4 j+p k, i-6 j+10 k and - i-3 j+7 k is 11 cubic units, then one of the...
- The shortest distance between the lines, where the first line passes through (0,0,0) and (2,0,3) and the second line passes...
- The point having position vector 4 i-11 j+2 k lies on the line
- 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
- If the vectors p i + j + k , i +q j + k and i + j +r k (p q r 1) are coplanar, then value of p q r – (p + q + r) is
- The scalar product of vectors a = i + 2 j + k and a unit vector along the sum of vectors b = 2 i - 4 j + 5 k and c = i + 2 j - 3...
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