The equation of the line through the point (0, 1, 2) and perpendicular to the line

$${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over { - 2}}$$ is :

Let $$\alpha$$ be the angle between the lines whose direction cosines satisfy the equations l + m $$-$$ n = 0 and l² + m² $$-$$ n² = 0. Then the value of sin⁴$$\alpha$$ + cos⁴$$\alpha$$ is :

Let a, b$$ \in $$R. If the mirror image of the point P(a, 6, 9) with respect to the line

$${{x - 3} \over 7} = {{y - 2} \over 5} = {{z - 1} \over { - 9}}$$ is (20, b, $$-$$a$$-$$9), then | a + b |, is equal to :

The vector equation of the plane passing through the intersection

of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {\widehat i - 2\widehat j} \right) = - 2$$, and the point (1, 0, 2) is :