Question

Find the value of c
please solve this question ​

Answer 1

If A and B are perpendicular vectors, then their DOT PRODUCT should be zero.

Dot product

• also called as scalar product.
• $\rm \vec{A}. \vec{B} = ABcos\theta$

Solution:

$\rightarrow\rm \vec{A} = 5\hat{i} +7\hat{j}-3\hat{k}$

$\rightarrow\rm \vec{B} = 2\hat{i} +2\hat{j}-c\hat{k}$

$\implies\rm \vec{A}. \vec{B} = ABcos90\degree$

$\implies \rm( 5\hat{i} +7\hat{j}-3\hat{k}).(2\hat{i} +2\hat{j}-c\hat{k})= 0$

$\implies\rm (5\times 2)(\hat{i}.\hat{i})+(7\times 2)(\hat{j}.\hat{j})+(-3\times {-c})(\hat{k}.\hat{k}) = 0$

$\implies \rm 10 + 14 + 3c = 0$

$\implies \rm 24 = - 3c$

$\implies \bf c = \dfrac {-24}{3} = - 8$

-------------------