Question

Assertion :The angle '$\theta$' between the lines whose DC's are $\frac{2}{7},\frac{3}{7},-\frac{6}{7}$ & $\frac{3}{5\sqrt{2}},\frac{-4}{5\sqrt{2}},\frac{5}{5\sqrt{2}}$ is ${\cos }^{-1}\left(\frac{-36}{35\sqrt{2}}\right)$ Reason: If ' $\theta$ ' be the angle between the line whose DC's are $l_1,m_1,n_1$ & $l_2,m_2,n_2$ , then $\cos \theta =l_1{l}_2+m_1{m}_2+n_1{n}_2$

• A. Assertion & Reason are true and Reason is the correct (proper) explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Assertion & Reason are true and Reason is the correct (proper) explanation of Assertion

Reason is true (from theory)
And using reason
$\cos \theta =l_1{l}_2+m_1{m}_2+n_1{n}_2$
$\Rightarrow \cos \theta =\frac{2}{7}\times 3\frac{3}{5\sqrt{2}}+\frac{3}{7}\left(\frac{-4}{5\sqrt{2}}\right)+\frac{-6}{7}\times \frac{5}{5\sqrt{2}}$
$\Rightarrow \cos \theta =\frac{6-12-30}{35\sqrt{2}}=\frac{-36}{35\sqrt{2}}\Rightarrow \theta ={\cos }^{-1}\left(\frac{-36}{35\sqrt{2}}\right)$
Hence assertion is also true