Vector `1/3 (2hati - 2hatj +hatk) ` is

Options

A. a unit vector
B. makes an angle `pi//3` with vector `(2hati- 4hatj + 3hatk) `
C. parallel to vector `( -hati + hatj - 1/2 hatk)`
D. perpendicular to vector `3hati + 2hatj - 2hatk`

Answer

a,c,d

Explanation

`veca=1/3(2hati-2hatj+hatk)`
`|veca|^(2)=1/9(4+4+1)=1or |veca|=1`
Let `vecb = 2hati - 4hatj + 3hatj`, then
` cos theta = (veca.vecb)/(|veca||vecb|) = 5/sqrt29 Rightarrow vecc ||veca`
Let `vecd = 3hati + 2hatj + 2hatk, " then " veca. vecd =0 Rightarrrow veca bot vecd`