A line with positive direction cosines passes through the point  A1,2,−1and makes equal angles with the coordinate axes. The line meets the plane  x+2y+z=5at the point B. Then the point Band length of the line segment AB¯respectively, are equal to

Equation of line passing through the point  A1,2,−1and making equal angles with axes, having positive direction ratios is x−1=y−2=z+1General point on the line is k+1,k+2,k−1Suppose that this point lies on the plane  x+2y+z=5It gives             k+1+2k+4+k−1=54k=1k=14Hence, the point of intersection of line and plane is B54,94,−34The distance between  A1,2,−1,B54,94,−34is  AB=116+116+116=34