Question

The volume of parallelopiped, whose coterminous edges are given by $\overline{u}=\hat{i}+\hat{j}+\lambda\hat{k}, \vec{v}=\hat{i}+\hat{j}+3\hat{k}, \overline{w}=2\hat{i}+\hat{j}+\hat{k}$ is 1 cu. units. If $\theta$ is the angle between $\overline{u}$ and $\overline{w}$, then the value of $\cos\theta$ is

• A. $\frac{3}{4}$
• B. $\frac{5}{6}$
• C. $\frac{1}{5}$
• D. $\frac{1}{6}$

Hint:

Logic Tip: The problem yields two possible values for $\lambda$ ($\lambda=2$ or $\lambda=4$). If $\lambda=4$, $\cos\theta = (2+1+4)/(\sqrt{18}\sqrt{6}) = 7/\sqrt{108} = 7/(6\sqrt{3})$, which isn't in the options. In multiple-choice questions, proceed immediately with the simplest integer root first; it usually maps to the correct option.

Answer 1

The Correct Option is B