Vectors

Question 1 Multiple Choice (Single Answer)

The vector equation of the line of intersection of the planes $r.(i+2j+3k)=0$ and $r.(3i+2j+k)=0$ is

$r=\lambda (i+2j+k)$
$r=\lambda (i-2j+k)$
$r=\lambda (i+2j-3k)$
None of these

Question 2 Multiple Choice (Single Answer)

Consider the planes $\displaystyle 3x-6y-2z=15$ and $\displaystyle 2x+y-2z=5.$

Assertion: The parametric equations of the line of intersection of the given planes are $\displaystyle x=3+14t, y=1+2t, z=15t.$ because

Reason: The vector $\displaystyle 14\hat{i}+2\hat{j}+15\hat{k}$ is parallel to the line of intersection of given planes.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Assertion is correct but Reason is incorrect
Both Assertion and Reason are incorrect

Question 3 Multiple Choice (Single Answer)

The ratio in which the line segment joining the points whose position vectors are $2\hat i-4\hat j-7\hat k$ and $-3\hat i+5\hat j-8\hat k$ is divided by the plane whose equation is $\hat r\cdot (\hat i-2\hat j+3\hat k)=13$ is-

$13:12$ internally
$12:25$ externally
$13:25$ internally
$37:25$ internally

Questions