A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.

Find the direction cosines of a line which makes equal angles with the coordinate axes.

Find the direction cosines of the line passing through the two points ( 2, 4, 5) and (1, 2, 3) .

A normal line with positive direction cosines to the plane P makes equal angles with the coordinate axis. The distance of the point A(1, 2, 3) from the line (x-1)/(1)=(y+2)/(1)=(z-3)/(2) measured parallel to the plane P is equal to

If the straight line passes through the point P(3,4) makes an angle pi/6 with x-axis and meets the line 12 x + 5 y + 10 = 0 at Q, Then the length of PQ is :

Find the direction cosines of the line passing through the two points (-1, 2, 3) and (2, -3, 5).

If the straight line through the point P(4,4) makes an angle pi/4 with x-axis and meets the line 12 x + 5 y + 10 = 0 at Q, Then the length of PQ is :

The direction cosines of the line passing through P(2,3,-1) and the origin are

If the straight line through the point (3,4) makes an angle pi/6 with x-axis and meets the line 12 x + 5 y + 10 = 0 at Q, Then the length of PQ is :

A line passing through the point (2, 2) encloses an area of 4 sq. units with coordinate axes. The sum of intercepts made by the line on the x and y axis is equal to