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1
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
Let $$\overrightarrow a = \widehat i - \alpha \widehat j + \beta \widehat k$$,   $$\overrightarrow b = 3\widehat i + \beta \widehat j - \alpha \widehat k$$ and $$\overrightarrow c = -\alpha \widehat i - 2\widehat j + \widehat k$$, where $$\alpha$$ and $$\beta$$ are integers. If $$\overrightarrow a \,.\,\overrightarrow b = - 1$$ and $$\overrightarrow b \,.\,\overrightarrow c = 10$$, then $$\left( {\overrightarrow a \, \times \overrightarrow b } \right).\,\overrightarrow c$$ is equal to ___________.
2
JEE Main 2021 (Online) 27th July Evening Shift
Numerical
+4
-1
The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points. Q(3, $$-$$4, $$-$$5) and R(2, $$-$$3, 1) and the plane 2x + y + z = 7, is equal to ______________.
3
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b$$ and $$\overrightarrow c = \widehat j - \widehat k$$ be three vectors such that $$\overrightarrow a \times \overrightarrow b = \overrightarrow c$$ and $$\overrightarrow a \,.\,\overrightarrow b = 1$$. If the length of projection vector of the vector $$\overrightarrow b$$ on the vector $$\overrightarrow a \times \overrightarrow c$$ is l, then the value of 3l2 is equal to _____________.
Let a plane P pass through the point (3, 7, $$-$$7) and contain the line, $${{x - 2} \over { - 3}} = {{y - 3} \over 2} = {{z + 2} \over 1}$$. If distance of the plane P from the origin is d, then d2 is equal to ______________.