Answer:
Option C
Explanation:
Concept involved if a x b= a x c
$\Rightarrow$ a x b-a x c=0
$\Rightarrow$ a x (b-c)=0 ie, a || (b-c)
or b-c= $\lambda $ a
Sol. Here, $a \times (2i+3j+4k)=(2i+3j+4k) \times b$
$\Rightarrow$ $a \times (2i+3j+4k)-(2i+3j+4k) \times b$
$\Rightarrow$ (a +b) x (2i+3j+4k)=0
$\Rightarrow$ $a+b=\lambda (2i+3j+4k)$.....(i)
since, $|a+b|= \sqrt{29}$
$\Rightarrow$ $\pm \lambda \sqrt{4+9+16}=\sqrt{29}$
$\Rightarrow$ $\lambda =\pm 1$
$\therefore$ a+b=$\pm (2i+3j+4k)$
Now, (a+b)(-7i+2j+3k)
=$ \pm (-14+6+-12)=\pm 4$