Let `veca (x) = (sin x) hati+ (cos x) hatj and vecb(x) = (cos 2x) hati + (sin 2x) hatj` be two variable vectors `( x in R)`. Then `veca (x) and vecb (x) ` are

Options

A. collinear for unique value of x
B. perpendicular for infinte values of x.
C. zero vectors for unique value of x
D. none of these

Answer

b

Explanation

if `veca ( x) and vecb are bot, "then" veca. Vecb =0`
`Rightarrow sin x cos 2x + cos x sin 2x =0`
`sin (3x) =0 = sin 0 `
` 3x = npi 0or x = (npi)/3`
therefore, the two vectors are `bot` for infinite values.