Question

Vectors along the adjacent sides of parallelogram are $\overrightarrow{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}$. Find the length of the longer diagonal of the parallelogram.

• A. $7$
• B. $1$
• C. $2$
• D. $\sqrt{5}$

Answer 1

The correct option is A $7$

Vectors along the sides are $\overrightarrow{a}=\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{b}=2\hat{i}+4\hat{j}+\hat{k}$
Let us find the equation of both the diagonals.
$\overrightarrow{a}-\overrightarrow{b}=-\hat{i}-2\hat{j}$
$\overrightarrow{a}+\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k}$
Hence, length of the longer diagonal is
$|\overrightarrow{a}+\overrightarrow{b}|=|3\hat{i}+6\hat{j}+2\hat{k}|=7$