1
IIT-JEE 1983
+1
-0.25
The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if
A
$$a=-40$$
B
$$a=40$$
C
$$a=20$$
D
none of these
2
IIT-JEE 1983
+1
-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
A
$${4 \over {13}}$$
B
$$4$$
C
$${2 \over 7}$$
D
none of these
3
IIT-JEE 1982
+2
-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
A
$$\overrightarrow a \,.\,\overrightarrow b = 0,\overrightarrow b \,.\,\overrightarrow c = 0$$
B
$$\overrightarrow b \,.\,\overrightarrow c = 0,\overrightarrow c \,.\,\overrightarrow a = 0$$
C
$$\overrightarrow c \,.\,\overrightarrow a = 0,\overrightarrow a \,.\,\overrightarrow b = 0$$
D
$$\overrightarrow a \,.\,\overrightarrow b = \overrightarrow b \,.\,\overrightarrow c = \overrightarrow c \,.\,\overrightarrow a = 0$$
4
IIT-JEE 1981
+2
-0.5
The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow A + \overrightarrow B + \overrightarrow C } \right)$$ equals :
A
$$0$$
B
$$\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right] + \left[ {\overrightarrow B \,\overrightarrow C \,\overrightarrow A } \right]$$
C
$$\left[ {\overrightarrow A \,\overrightarrow B \,\overrightarrow C } \right]$$
D
None of these
EXAM MAP
Medical
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