1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus
For real numbers $$\alpha$$ and $$\beta$$ $$\ne$$ 0, if the point of intersection of the straight lines

$${{x - \alpha } \over 1} = {{y - 1} \over 2} = {{z - 1} \over 3}$$ and $${{x - 4} \over \beta } = {{y - 6} \over 3} = {{z - 7} \over 3}$$, lies on the plane x + 2y $$-$$ z = 8, then $$\alpha$$ $$-$$ $$\beta$$ is equal to :
A
5
B
9
C
3
D
7
2
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus
Let the plane passing through the point ($$-$$1, 0, $$-$$2) and perpendicular to each of the planes 2x + y $$-$$ z = 2 and x $$-$$ y $$-$$ z = 3 be ax + by + cz + 8 = 0. Then the value of a + b + c is equal to :
A
3
B
8
C
5
D
4
3
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Out of Syllabus
Let the foot of perpendicular from a point P(1, 2, $$-$$1) to the straight line $$L:{x \over 1} = {y \over 0} = {z \over { - 1}}$$ be N. Let a line be drawn from P parallel to the plane x + y + 2z = 0 which meets L at point Q. If $$\alpha$$ is the acute angle between the lines PN and PQ, then cos$$\alpha$$ is equal to ________________.
A
$${1 \over {\sqrt 5 }}$$
B
$${{\sqrt 3 } \over 2}$$
C
$${1 \over {\sqrt 3 }}$$
D
$${1 \over {2\sqrt 3 }}$$
4
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
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Class 12