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1
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let P be a plane containing the line $${{x - 1} \over 3} = {{y + 6} \over 4} = {{z + 5} \over 2}$$ and parallel to the line $${{x - 1} \over 4} = {{y - 2} \over { - 3}} = {{z + 5} \over 7}$$. If the point (1, $$-$$1, $$\alpha$$) lies on the plane P, then the value of |5$$\alpha$$| is equal to ____________.
2
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, $$-$$3, 1) and (2, 3, $$-$$5) at the right angles. If a, b, c, d are integers, then the
minimum value of (a2 + b2 + c2 + d2) is
3
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
The equation of the planes parallel to the plane x $$-$$ 2y + 2z $$-$$ 3 = 0 which are at unit distance from the point (1, 2, 3) is ax + by + cz + d = 0. If (b $$-$$ d) = K(c $$-$$ a), then the positive value of K is
Let $$\overrightarrow x$$ be a vector in the plane containing vectors $$\overrightarrow a = 2\widehat i - \widehat j + \widehat k$$ and $$\overrightarrow b = \widehat i + 2\widehat j - \widehat k$$. If the vector $$\overrightarrow x$$ is perpendicular to $$\left( {3\widehat i + 2\widehat j - \widehat k} \right)$$ and its projection on $$\overrightarrow a$$ is $${{17\sqrt 6 } \over 2}$$, then the value of $$|\overrightarrow x {|^2}$$ is equal to __________.