# Coordinate Geometry – Exercise – 1

1. The pair of lines whose direction cosines are given by the equations 3l+m+5n=0, 6mn-2nl+5lm=0 are :

(a) parallel
(b) perpendicular
(c) inclined at cos-1 (1/6)
(d) none of these

Explanation
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2. The angle between any two diagonals of a cube is :

(a) cos θ = √3/2
(b) cos θ = 1/√2
(c) cos θ = 1/3
(d) cos θ = 1/√6

Explanation
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3. The point equidistant from the four points (a,0,0), (0,b,0), (0,0,c) and (0,0,0) is :

(a) (a,b,c)
(b) (a/2,b/2,c/2)
(c) (a/3,b/3,c/3)
(d) None of these

Explanation
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4. The line joining the points (1,1,2) and (3, -2 ,1) meets the plane 3x+2y+z = 6 at the point :

(a) (1,1,2 )
(b) (3,-2 ,1)
(c) (2,-3,1 )
(d) (3,2 ,1)

Explanation
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5. The plane passing through the point (5,1,2) perpendicular to the line
2(x-2) = y-4 = z-5 will meet the line in the point :

(a) (1,2 ,3)
(b) (2,3,1 )
(c) (1,3 ,2)
(d) (3,2,1 )