Question

$\overline{a}=x\hat{i}+y\hat{j}+z\hat{k},\overline{b}=\hat{j}$, then the vector $\overline{c}$ for which $\overline{a},\overline{b},\overline{c}$ form a right hand triangle

• A. $x(\hat{i}-\hat{k})$
• B. $\hat{0}$
• C. $-z\hat{i}+x\hat{k}$
• D. $y\hat{j}$

Answer 1

Answer: (C)

$-z\hat{i}+x\hat{k}$

$\overline{a},\overline{b},\overline{c}$ form a right handed triangle.
When this holds true, $\overline{c}=\overline{a}\times \overline{b}$
Thus, taking cross product , we get $\overline{c}=-z\overline{i}+x\overline{k}$