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1
JEE Main 2021 (Online) 20th July Morning Shift
Numerical
+4
-1
If the shortest distance between the lines $$\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k + \lambda (\widehat i - 2\widehat j + 2\widehat k)$$, $$\lambda$$ $$\in$$ R, $$\alpha$$ > 0 and $$\overrightarrow {{r_2}} = - 4\widehat i - \widehat k + \mu (3\widehat i - 2\widehat j - 2\widehat k)$$, $$\mu$$ $$\in$$ R is 9, then $$\alpha$$ is equal to ____________.
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2
JEE Main 2021 (Online) 18th March Evening Shift
Numerical
+4
-1
Let the mirror image of the point (1, 3, a) with respect to the plane $$\overrightarrow r .\left( {2\widehat i - \widehat j + \widehat k} \right) - b = 0$$ be ($$-$$3, 5, 2). Then, the value of | a + b | is equal to ____________.
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3
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 ____________.
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4
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
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