Unit vector If A vector x cap4 y cap2 z cap and B vector

Unit vector

If A vector = x cap4 - y cap2 + z cap and B vector is a unit vector Find: Vector B such that B is parallel to vector A. Vector B such that B is perpendicular to vector A, if B is in the xy plane.

Solution

a)

||A||=\\sqrt{4^2+2^2+1^2)=sqrt{21}

So,

B=A/sqrt{21}

b)

Let, B=xi+yj

So, A.B=0

4x-2y=0

Hence, y=2x

Also

x^2+y^2=1

x^2+4x^2=1

x=1/sqrt{5}

y=2/sqrt{5}

Hence,

B=i/sqrt{5}+2j/sqrt{5}