Question

If `R^2` if the magnitude of the projection vector of the vecrtor `alphahati+betahatj on sqrt(3) hati+hatj is sqrt(3)` and if `alpha=2+sqrt(3)beta` then possible value (s) of `|alpha|` is /are
A. 1,2
B. 3,4
C. 4,5
D. 3

Answer 1

Correct Answer - D
Let `veca = alpha hati + betahati and vecb = sqrt3hati + hatj` , It is given that the magnitude of projection of `veca " on " vecb " is " sqrt3` .
` |(veca.vecb)/(|veca|)|= sqrt3`
` Rightarrow |(sqrt3 alpha + beta)/2| = sqr3 Rightarrow sqrt3 alpha + beta = +- 2sqrt3`
` Rightarrow sqrt3 ( 2 + sqrt3 beta) + beta = -+ 2sqrt3`
` Rightarrow 2sqrt3 + 4beta = -+ 2sqrt3`
` Rightarrow beta =0 or, beta = sqrt3`
Substituting these values in ` alpha = 2 sqrt3 beta`, we obtain ` alpha =2 or alpha =1`