Browse Questions

# The sides of a parallelogram are given by vectors $2\hat i+4\hat j-5\hat k$ and $\hat i+2\hat j+3\hat k$. Unit vector along one of the diagonals is given by ?

$\begin{array}{1 1} \large\frac{3\hat i-6\hat j-2\hat k}{7}\\\large\frac{3\hat i+6\hat j-2\hat k}{7} \\ \large\frac{-3\hat i+6\hat j-2\hat k}{7} \\ \large\frac{3\hat i+6\hat j+2\hat k}{7}\end{array}$

According to parallelogram law of addition ,
$\overrightarrow a+\overrightarrow b$ and $\overrightarrow a-\overrightarrow b$ are the
diagonals of the parallelogram if $\overrightarrow a$ and $\overrightarrow b$ are adjacent sides.
Given: $\overrightarrow a=2\hat i+4\hat j-5\hat k$ and $\overrightarrow b=\hat i+2\hat j+3\hat k$
$\overrightarrow a+\overrightarrow b=3\hat i+6\hat j+2\hat k$
Unit vector along diagonal = $\large\frac{3\hat i+6\hat j-2\hat k}{7}$