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