`3hati+4hatj+12hatk` is a vector. Find the magnitude of the vector and the angles it makes with x,y and z axes.

Explanation

If `vecr=xhati+yhatj+zhatk,` then the magnitude `|vecr|=sqrt(x^2+y^2+z^2)`
`therefore` Magnitude of the vector `3hati+4hatj+12hatk` is,
`a=sqrt(3^2+4^2+12^2)=sqrt(169)=13`
Let the corresponding angles the vector makes with the x,y and z axes be `alpha, beta and gamma` respectively.
From definitions,
`cos alpha=x/a=3/(13) or,alpha=cos^(-1)""(3)/(13)`
`cos beta=y/a=4/(13) or, beta =cos^(-1)""4/(13)`
`and cos gamma =z/z=(12)/(13) or,gamma=cos^(-1)""(12)/(13)`.