IIT-JEE 1994 | 3D Geometry Question 51 | Mathematics

IIT-JEE 1994

MCQ (Single Correct Answer)

-1

Let $$\overrightarrow p $$ and $$\overrightarrow q $$ be the position vectors of $$P$$ and $$Q$$ respectively, with respect to $$O$$ and $$\left| {\overrightarrow p } \right| = p,\left| {\overrightarrow q } \right| = q.$$ The points $$R$$ and $$S$$ divide $$PQ$$ internally and externally in the ratio $$2:3$$ respectively. If $$OR$$ and $$OS$$ are perpendicular then

$$9{q^2} = 4{q^2}$$

$$4{p^2} = 9{q^2}$$

$$9p = 4q$$

$$4p = 9q$$

IIT-JEE 1983

MCQ (Single Correct Answer)

-0.25

The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if

$$a=-40$$

$$a=40$$

$$a=20$$

none of these

IIT-JEE 1983

MCQ (Single Correct Answer)

-0.25

The volume of the parallelopiped whose sides are given by
$$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i + j - k,\,\overrightarrow {OC} = 3i - k,$$ is

$${4 \over {13}}$$

$$4$$

$${2 \over 7}$$

none of these

JEE Advanced Subjects