Discussion Forum

lf a and b are vectors such that |a+b|=$\sqrt{29}$ and $a \times (2 i+3j+4k)=(2i+3j+4k) \times b$ the  a possible value of $(a+b).(-7 i+2j+3k)$ is 

Answer:

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)

 =$\pm (-14+6+-12)=\pm 4$