Question

Assertion :The lines $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-2}$ are coplanar Reason: If two lines are perpendicular to each other, then these are coplanar.

• A. Assertion is True, reason is True; reason is a correct explanation for assertion
• B. Assertion is True, reason is True; reason is Not a correct explanation for assertion
• C. Assertion is True, reason is False
• D. Assertion is False, reason is True

Answer 1

The correct option is C Assertion is True, reason is False

Given line $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-2}$

formula used

$\left|\begin{array}{ccc}{x}_2-x_1& y_2-y_1& z_2-z_1\\ a_1& b_1& c_1\\ a_2& b_2& c_2\end{array}\right|$

are co planar

Hence determinant

$=\left|\begin{array}{ccc}1-1& 3-3& 4.4\\ 3& 4& 5\\ 3& 1& -2\end{array}\right|$

$=\left|\begin{array}{ccc}0& 0& 0\\ 3& 4& 5\\ 3& 1& -2\end{array}\right|=0$ [one Row of det. is zero hence $=0$]

So the lines are coplanar

means Assertion is right

Two line are are perpendicular they can't line in same plane hence Reason is wrong Assertion is true reason is false.