Question

For any vector $r$ $i\times (r\times i)+j\times (r\times j)+k\times (r\times k)$ is equal to

• A. 0
• B. 2 r
• C. 3 r
• D. 4 r

Answer 1

Answer: (B)

Now, $i\times (r\times i)$
$=(i\cdot i)r-(i\cdot r)i$
$=r-r_{1}i$
Similarly, $j\times (r\times j)=r-r_{2}j$
and $k\times (r\times k)=r-r_{3}k$
$\therefore (i\times (r\times i))+(j\times (r\times j))+(k\times (r\times k))$
$=3r-\left(r_{1}i+r_{2}j+r_{3}k\right)$
$=3r-r=2r$