Question

Assertion :If vectors $a$ and $c$ are non collinear then the lines $r=6a-c+\lambda (2c-a)$ and $r=a-c+\mu (a+3c)$ are coplanar Reason: There exist $\lambda$ and $\mu$ such that the two values of $r$ become same.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

equate given two equations , we get $5a=a(\mu +\lambda )+c(3\mu -2\lambda )$.

$a(5-\lambda -\mu )=c(3\mu -2\lambda )$.

now slve $3\mu -2\lambda =0$ and $5-\lambda -\mu =0$.

we get $\lambda =3$ and $\mu =2$.

Therefore there exists $\mu$ and $\lambda$ such that two values of $r$ is equal.

so the two lines are coplanar.

Both assertion and reason are correct and reason is correct explanation for assertion.