Question

If the angle between $\overline{a}=\lambda \hat{i}-3\hat{j}-k,\overline{b}=2\lambda \hat{i}+\lambda \hat{j}-k$, is acute and $\overline{b}$ makes obtuse angle with the axes of its coordinate, then $\lambda ϵ$ ____.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\overline{a}.\overline{b}$ $\Rightarrow$ ${2\lambda }^2$-$3\lambda$+1 > 0 $\Rightarrow$ $\lambda$ < $\frac{1}{2}$ or $\lambda$ > 1 ....(1)

$\overline{b}.i$<0, $\overline{b}.j$<0, $\overline{b}.k$<0 $\Rightarrow$ $\lambda$ < 0 ..... (2)

From (1) and (2), $\lambda ϵ(-\infty ,0)$