" If "P(1,y,z)" lies on the line through "(3,2,-1)" and "(-4,6,3)," find "y&z

If A ( 1 , y , z) lies on the line through the points b ( 3 , 2 , - 1) and c ( - 4 , 6 , 3) , then find the values of y and z .

A point P lies on a line through Q(1,-2,3) and is parallel to the line (x)/(1)=(y)/(4)=(z)/(5) . If P lies on the plane 2x+3y-4z+22=0 , then segment PQ equal to

(i) Find the value of 'p' so that the lines : l_(1) : (1 - x)/(3) = (7y -14)/(2p) = (z - 3)/(2) and l_(2) : (7 -7x)/(3p) = (y - 5)/(1) = (6 - z)/(5) are at right angles. Also, find the equations of the line passing through (3,2, -4) and parallel to line l_(1) . (ii) Find 'k' so that the lines : (x - 3)/(2) = (y + 1)/(3 ) = (z - 2)/(2k) and (x + 2)/(1) = (4 -y)/(k) = (z + 5)/(1) are perpendicular to each other.

Find the equation of the line through point (1,2,3) and parallel to line x-y+2z5,3x+y+z=6 .

Find the equation of the line through point (1,2,3) and parallel to line x-y+2z=5,3x+y+z=6 .

Find the equation of the line through point (1,2,3) and parallel to line x-y+2z=5,3x+y+z=6