1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Out of Syllabus
Let L be the line of intersection of planes $$\overrightarrow r .(\widehat i - \widehat j + 2\widehat k) = 2$$ and $$\overrightarrow r .(2\widehat i + \widehat j - \widehat k) = 2$$. If $$P(\alpha ,\beta ,\gamma )$$ is the foot of perpendicular on L from the point (1, 2, 0), then the value of $$35(\alpha + \beta + \gamma )$$ is equal to :
A
101
B
119
C
143
D
134
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
+4
-1
Out of Syllabus
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?
A
($$-$$1, 1, 2)
B
(1, 1, 1)
C
(1, 1, 2)
D
(1, 2, 2)
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