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A line passes through the points (6,-...

A line passes through the points `(6,-7,-1)a n d(2,-3,1)dot` Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

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Let `l, m and n` be the direction cosines of the given line. As it makes an acute angle with the x-axis, `l gt 0`. The line passes through (6, -7, -1) and (2, -3, 1), therefore, its direction ratios are (6, -2, -7+3, -1-1) or (4, -4, -2). Hence, the direction cosines of the given line are 2/3, -2/3 and -1/3.
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