Correct Answer - Option 3 :
\(\frac{1}{3},\frac{2}{3},\frac{2}{3}\)
Concept:
The direction cosine of the line segment joining the points P(x1, y1, z1) and Q(x2, y2, z2) are \(\frac{x_2 -x_1}{PQ} , \frac{y_2 -y_1}{PQ} , \frac{z_2 -z_1}{PQ}\)
where \(PQ = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2+ (z_2 - z_1)^2}\)
Calculation:
Let given point P = (1, 1, -1) & Q = (2, 3, 1)
\(PQ = \sqrt{ (2-1)^2 + (3-1)^2 + ( 1+1 )^2}\)
\(PQ = \sqrt{1^2 + 2^2 + 2^2}\)
\(PQ = \sqrt{1+4+4}\) = \(\sqrt{9}\) = 3
Hence, the direction cosines of the line joining two points are:
\(\frac{1}{3}, \frac{2}{3}, \frac{2}{3}\)
