Find the angle between the vector `vecr_(1)=(4hati-3hatj+5hatk) andvecr_(2)=(3hati+4hatj+5hatk)`.

Explanation

Let `theta` be the angle between `vecr_(1) and vecr_(2)`. Then,
`costheta=(vecr_(1)*vecr_(2))/(|vecr_(1)||vecr_(2)|)=((4hati-3hatj+5hatk)*(3hati+4hatj+5hatk))/({sqrt(4^(2)+(-3)^(2)+5^(2))}{sqrt(3^(2)+4^(2)+5^(2))})`
`((12-12+25))/({sqrt(16+9+25)}{sqrt(9+16+25)})=(25)/({sqrt50xxsqrt50})=(25)/(50)=(1)/(2)`.
`therefore theta=cos^(-1)((1)/(2))=(pi)/(3)`.
Hence, the angle between the given vectors is `(pi)/(3)`.