1
IIT-JEE 1983
Subjective
+2
-0
A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate system $$oxyz.$$ The coordinate system is rotated about the $$x$$-axis through an angle $${\pi \over 2}.$$ Find the components of $$A$$ in the new coordinate system in terms of $${A_1},{A_2},{A_3}.$$
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+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
3
IIT-JEE 1983
MCQ (Single Correct Answer)
+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
4
IIT-JEE 1983
True or False
+1
-0
If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,C} \right] = 0$$
A
TRUE
B
FALSE
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