If θ is the angle between any two vectors a and b, then ∣∣a.b∣∣=∣∣a×b∣∣ when θ is equal to(A) 0 (B) 4π (C) 2π (D) π
What is the unit vector parallel to a=3i^+4j^−2k^ ? What vector should be added to a so that the resultant is the unit vector i^?
Statement 1: if three points P,QandR have position vectors a,b,andc , respectively, and 2a+3b−5c=0, then the points P,Q,andR must be collinear. Statement 2: If for three points A,B,andC,AB=λAC, then points A,B,andC must be collinear.
ABCD is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and OA+OB+OC+OD=xOE,thenx is equal to a. 3 b. 9 c. 7 d. 4
If in parallelogram ABCD, diagonal vectors are AC=2i^+3j^+4k^ and BD=−6i^+7j^−2k^, then find the adjacent side vectors AB and AD
The vector a has the components 2p and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel about the origin in the counterclockwise sense. If, with respect to a new system, a has components (p+1)and1 , then p is equal to a. −4 b. −1/3 c. 1 d. 2