IIT-JEE 1983 | Vector Algebra and 3D Geometry Question 153 | Mathematics

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

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 1982

MCQ (Single Correct Answer)

-0.5

For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right).\overrightarrow c } \right| = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|$$ holds if and only if

$$\overrightarrow a \,.\,\overrightarrow b = 0,\overrightarrow b \,.\,\overrightarrow c = 0$$

$$\overrightarrow b \,.\,\overrightarrow c = 0,\overrightarrow c \,.\,\overrightarrow a = 0$$

$$\overrightarrow c \,.\,\overrightarrow a = 0,\overrightarrow a \,.\,\overrightarrow b = 0$$

$$\overrightarrow a \,.\,\overrightarrow b = \overrightarrow b \,.\,\overrightarrow c = \overrightarrow c \,.\,\overrightarrow a = 0$$

IIT-JEE 1981

MCQ (Single Correct Answer)

-0.5

The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow A + \overrightarrow B + \overrightarrow C } \right)$$ equals :

$$0$$

$$\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right] + \left[ {\overrightarrow B \,\overrightarrow C \,\overrightarrow A } \right]$$

$$\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right]$$

None of these

JEE Advanced Subjects