Question

If '$\lambda$' for the vectors $2i+3j-4k$ & $4i-2j+\lambda k$ are orthogonal is $\frac{1}{m}$

Answer 1

For orthogonal vectors,dot product$=0$

$⟹(2\stackrel{\wedge }{i}+3\stackrel{\wedge }{j}-4\stackrel{\wedge }{k}).(4\stackrel{\wedge }{i}-2\stackrel{\wedge }{j}+\lambda \stackrel{\wedge }{k})=0$

$⟹8-6-4\lambda =0$

$⟹2=4\lambda$

$⟹\lambda =\frac{1}{2}$

$\therefore \frac{1}{m}=\frac{1}{2}$

$⟹m=2$