Find a vector of magnitude 5 units, and parallel to the resultant of the vectors `veca = 2i + 3hatj - hatk` and `vecb = hati - 2hatj + hatk`
If `veca` is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λ`veca` is unit vector if
(A) λ = 1 (B) λ = –1
(C) a = |λ|
(D) a = 1/|λ|
Find a vector `veca` of magnitude 5√2 , making an angle of π/4 with x-axis, π/2 with y-axis and an acute angle θ with z-axis.
If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, show that the vector `veca + vecb+ vecc` is equally inclined to `veca, vecb` and `vecc`.
Find the magnitude of two vectors `veca and vecb` , having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2