If the line $${{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}$$ lies on the plane $$2x - 4y + z = 7$$, then what is the value of k?

A point on the line $${{x - 1} \over 1} = {{y - 3} \over 2} = {{z + 2} \over 7}$$ has coordinates

If the points (x, y, $$-$$3), (2, 0, $$-$$1) and C (4, 2, 3) lie on a straight line, then what are the values of x and y respectively?

A straight line passes through the point (1, 1, 1) makes an angle 60$$^\circ$$ with the positive direction of Z-axis, and the cosine of the angles made by it with the positive directions of the Y-axis and the X-axis are in the ratio $$\sqrt 3 $$ : 1. What is the acute angle between the two possible positions of the line?