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Question: A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of line, so direc...

A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of line, so directed that the angle made by it with the positive direction of x-axis is acute, are

A

23,−23,−13\frac { 2 } { 3 } , \frac { - 2 } { 3 } , \frac { - 1 } { 3 }

B

−23,23,13\frac { - 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 }

C

23,−23,13\frac { 2 } { 3 } , \frac { - 2 } { 3 } , \frac { 1 } { 3 }

D

23,23,13\frac { 2 } { 3 } , \frac { 2 } { 3 } , \frac { 1 } { 3 }

Answer

23,−23,−13\frac { 2 } { 3 } , \frac { - 2 } { 3 } , \frac { - 1 } { 3 }

Explanation

Solution

Let l, m, n be the d.c.’s of a given line.

Then, as it makes an acute angle with x-axis, therefore l>0.

Direction ratios = 4, –4, –2 or 2, –2, –1 and

Direction cosines =23,−23,−13\frac { 2 } { 3 } , \frac { - 2 } { 3 } , \frac { - 1 } { 3 }.