1
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let a, b c $$\in$$ R be such that a2 + b2 + c2 = 1. If
$$a\cos \theta = b\cos \left( {\theta + {{2\pi } \over 3}} \right) = c\cos \left( {\theta + {{4\pi } \over 3}} \right)$$,
where $${\theta = {\pi \over 9}}$$, then the angle between the vectors $$a\widehat i + b\widehat j + c\widehat k$$ and $$b\widehat i + c\widehat j + a\widehat k$$ is :
A
0
B
$${{\pi \over 9}}$$
C
$${{{2\pi } \over 3}}$$
D
$${{\pi \over 2}}$$
2
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
The lines
$$\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)$$ and
$$\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} \right)$$
A
do not intersect for any values of $$l$$ and m
B
intersect for all values of $$l$$ and m
C
intersect when $$l$$ = 2 and m = $${1 \over 2}$$
D
intersect when $$l$$ = 1 and m = 2
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let $$\overrightarrow a = \widehat i - 2\widehat j + \widehat k$$ and $$\overrightarrow b = \widehat i - \widehat j + \widehat k$$ be two vectors. If $$\overrightarrow c$$ is a vector such that $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow a$$ and $$\overrightarrow c .\overrightarrow a = 0$$, then $$\overrightarrow c .\overrightarrow b$$ is equal to
A
$$- {1 \over 2}$$
B
$$- {3 \over 2}$$
C
$${1 \over 2}$$
D
-1
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Let the volume of a parallelopiped whose coterminous edges are given by

$$\overrightarrow u = \widehat i + \widehat j + \lambda \widehat k$$, $$\overrightarrow v = \widehat i + \widehat j + 3\widehat k$$ and

$$\overrightarrow w = 2\widehat i + \widehat j + \widehat k$$ be 1 cu. unit. If $$\theta$$ be the angle between the edges $$\overrightarrow u$$ and $$\overrightarrow w$$ , then cos$$\theta$$ can be :
A
$${7 \over {6\sqrt 3 }}$$
B
$${7 \over {6\sqrt 6 }}$$
C
$${5 \over 7}$$
D
$${5 \over {3\sqrt 3 }}$$
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