Solution: Given that, The vertices are $(3,5,-4),(-1,1,2)$ and $(-5,-5,-2)$. Firstly find the direction ratios of $\mathrm{AB}$ Where, $A=(3,5,-4)$ and $B=(-1,1,2)$ Ratio of $A...
Show that the points (2, 3, 4), (–1, –2, 1), (5, 8, 7) are collinear.
Solution: If the direction ratios of two lines segments are proportional, then the lines are collinear. It is given that $\mathrm{A}(2,3,4), \mathrm{B}(-1,-2,1), \mathrm{C}(5,8,7)$ The direction...
If a line has the direction ratios –18, 12, –4, then what are its direction cosines?
Solution: Given that, The direction ratios are $-18,12,-4$ Where, $a=-18, b=12, c=-4$ Consider the direction ratios of the line as $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ Direction cosines are...
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Solution: Given that, Angles are equal. Let the angles be $\alpha, \beta, \mathrm{Y}$ The direction cosines of the line be I, $\mathrm{m}$ and $\mathrm{n}$ $I=\cos \alpha, m=\cos \beta \text { and }...
If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines.
Solution: Let's consider the direction cosines of the line be $I, m$ and $n$. Let $\alpha=90^{\circ}, \beta=135^{\circ}$ and $\mathrm{y}=45^{\circ}$ Therefore, $I=\cos \alpha, m=\cos \beta \text {...