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?

A point on a line has coordinates (p + 1, p $$-$$ 3, $$\sqrt 2 $$p) where p is any real number. What are the direction cosines of the line?

The centroid of the triangle with vertices A(2, $$-$$3, 3), B(5, $$-$$3, $$-$$4) and C(2, $$-$$3, $$-$$2) is the point

What is the radius of the sphere $${x^2} + {y^2} + {z^2} - 6x + 8y - 10z + 1 = 0$$ ?