The vectors a and bare not perpendicular and cand dare two vectors satisfying : b×c=b×d,a⋅d=0. Then the vector dis equal to :
If the vertices A, B, C of a triangle ABC are (1,2,3),(1,0,0),(0,1,2), respectively, then find ∠ABC. [∠ABCis the angle between the vectors BAand BC.
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are 31,31,31.
Area of a rectangle having vertices A, B, C and D with position vectors −i^+21j^+4k^,i^+21j^+4k^,i^−21j^+4k^ and −i^−21j^+4k^ respectively is
(A) 1/2 (B) 1 (C) 2 (D) 4
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
Consider two points P and Q with position vectors →OP=3→a−2→band →OQ=→a+→bFind the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.
If with reference to the right handed system of mutually perpendicular unit vectors i^,j^and k^, →α=3i^−j^,→β=2i^+j^−3k^, then express →βin the from →β=→β1+→β2, where \displaystyle-