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A vector is given by vec (A) = 3 hat(i) ...

A vector is given by `vec (A) = 3 hat(i) + 4 hat(j) + 5 hat(k)`. Find the magnitude of `vec(A)` , unit vector along `vec(A)` and angles made by `vec(A)` with coordinate axes.

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We have ,mangnitude `|A|=A=sqrt(A_(x)^(2)+A_(y)^(2)+A_(z)^(2))`
`sqrt((3)^(2)+(4)^(2)+(t)^(2))=5sqrt(2)`
`"unit vector,"hatA=(A)/(|A|)=(3hati+4hatj+5hatk)/(5sqrt(2))`
Angles made by A with coordinateaxis
`cosalpha=(A_(x))/(|A|)=(3)/(5sqrt(2))implies alpha=cos^(-1)((3)/(5sqrt(2)))`
`costheta=(A)/(|A|)=(4)/(5sqrt(2))impliesbeta= cos^(-1)((4)/(5sqrt(2)))`
`cosgamma=(A_(z))/(|A|)=(5)/(5sqrt(2))`
`gamma=cos^(-1)((1)/(sqrt(2)))=(pi)/(4)`
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