Vector Algebra questions
907 published questions with worked solutions.
- a ( b c), b ( c a) and c ( a b) are
- If the vectors a, b, c and d are coplanar then ( a b) ( c d) is equal to
- If a ( a b)= b ( b c) and a b 0 then [ a b c] is equal to
- Let OA = a, OB =10 a+2 b and OC = b, where O, A and C are noncollinear points. Let p denote the area of the quadrilateral OABC,...
- P is a point on the line through the point A whose position vector is a and the line is parallel to the vector b. If PA=6, the...
- Let AB =3 i+ j- k and AC = i- j+3 k. If the point P on the line segment BC is equidistant from AB and AC then AP is
- If AB = b and AC = c then the length of the perpendicular from A to the line BC is
- If the vertices of a tetrahedron have the position vectors 0, i+ j, 2 j- k and i+ k then the volume of the tetrahedron is
- A line passes through the points whose position vectors are i+ j-2 k and i-3 j+ k. The position vector of a point on it at a unit...
- A vector of magnitude 2 along a bisector of the angle between the two vectors 2 i-2 j+ k and i+2 j-2 k is
- A unit vector coplanar with i+ j+2 k and i+2 j+ k, and perpendicular to i+ j+ k, is
- If | a|=4, | b|=2 and the angle between a and b is 6 then ( a b)^2 is equal to
- Three points whose position vectors are a, b, c will be collinear if
- Let b=4 i+3 j. Let c be a vector perpendicular to b and it lies in the x-y plane. A vector in the x-y plane having projections 1...
- If a, b, c are noncoplanar vectors such that b c= a, a b= c and c a= b then
- Let a, b, c be noncoplanar vectors and p= b c [ a b c] , q= c a [ b c a] , r= a b [ c a b] then
- If a, b, c are any three vectors then ( a b) c is a vector
- If c= a b and b= c a then
- If x b= c b and x a then x is equal to
- The resolved part of the vector a along the vector b is and that perpendicular to b is . Then
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