Javascript is required
1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let three vectors $$\overrightarrow a$$, $$\overrightarrow b$$ and $$\overrightarrow c$$ be such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c$$, $$\overrightarrow b \times \overrightarrow c = \overrightarrow a$$ and $$\left| {\overrightarrow a } \right| = 2$$. Then which one of the following is not true?
A
$$\overrightarrow a \times \left( {(\overrightarrow b + \overrightarrow c ) \times (\overrightarrow b \times \overrightarrow c )} \right) = \overrightarrow 0$$
B
Projection of $$\overrightarrow a$$ on $$(\overrightarrow b \times \overrightarrow c )$$ is 2
C
$$\left[ {\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } } \right] + \left[ {\matrix{ {\overrightarrow c } & {\overrightarrow a } & {\overrightarrow b } \cr } } \right] = 8$$
D
$${\left| {3\overrightarrow a + \overrightarrow b - 2\overrightarrow c } \right|^2} = 51$$
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
If the shortest distance between the straight lines $$3(x - 1) = 6(y - 2) = 2(z - 1)$$ and $$4(x - 2) = 2(y - \lambda ) = (z - 3),\lambda \in R$$ is $${1 \over {\sqrt {38} }}$$, then the integral value of $$\lambda$$ is equal to :
A
3
B
2
C
5
D
$$-$$1
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
The lines x = ay $$-$$ 1 = z $$-$$ 2 and x = 3y $$-$$ 2 = bz $$-$$ 2, (ab $$\ne$$ 0) are coplanar, if :
A
b = 1, a$$\in$$R $$-$$ {0}
B
a = 1, b$$\in$$R $$-$$ {0}
C
a = 2, b = 2
D
a = 2, b = 3
4
JEE Main 2021 (Online) 20th July Evening Shift
Consider the line L given by the equation $${{x - 3} \over 2} = {{y - 1} \over 1} = {{z - 2} \over 1}$$. Let Q be the mirror image of the point (2, 3, $$-$$1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P?
($$-$$1, 1, 2)