Find the area of the parallelogram whose adjacent sides are determined by the vectors a=i^−j^+3k^ and b=2i^−7j^+k^.
If the vectors 3p+q;5p−3qand2p+q;4p−2q are pairs of mutually perpendicular vectors, then find the angle between vectors pandq˙
Column I, Column II Collinear vectors, p.a Coinitial vectors, q. b Equal vectors, r. c Unlike vectors (same intitial point), s. d
Let a,bandc be unit vectors, such that a+b+c=x,ax˙=1,bx˙=23,∣x∣=2. Then find the angel between and ×˙
The axes of coordinates are rotated about the z-axis though an angle of π/4 in the anticlockwise direction and the components of a vector are 22, 32,4. Prove that the components of the same vector in the original system are -1,5,4.
Vectors a=−4i^+3k^;b=14i^+2j^−5k^ are laid off from one point. Vector d^ , which is being laid of from the same point dividing the angle between vectors aandb in equal halves and having the magnitude 6, is a. i^+j^+2k^ b. i^−j^+2k^ c. i^+j^−2k^ d. 2i^−j^−2k^
If the vectors i^−j^,j^+k^anda form a triangle, then a may be a. −i^−k^ b. i^−2j^−k^ c. 2i^+j^+k^ d. i^+k^