First slide

Direction ratios and direction cosines

Question

If $O P = 10 \sqrt{2}$ and direction cosines of $\vec{O P}$ are $(\frac{3 \sqrt{2}}{10}, \frac{4 \sqrt{2}}{10}, \frac{5 \sqrt{2}}{10})$ , then

Easy

A

$(3, 4, 5)$
B

$(- 3, - 4, - 5)$
C

$(- 3, - 4, 5)$
D

$(6, 8, 10)$

Solution

If the length of the line segment $O P = r$ and direction cosines of $\bar{O P}$ are $〈l, m, n〉$ then the coordinates of the point $P (l r, m r, n r)$
Here, $(l, m, n) = (\frac{3 \sqrt{2}}{10}, \frac{4 \sqrt{2}}{10}, \frac{5 \sqrt{2}}{10})$ and $r = 10 \sqrt{2}$
Therefore, the coordinates of the point $P$ are as below.
Here , $P (\frac{3 \sqrt{2}}{10} \cdot 10 \sqrt{2}, \frac{4 \sqrt{2}}{10} \cdot 10 \sqrt{2}, \frac{5 \sqrt{2}}{10} \cdot 10 \sqrt{2}) = (6, 8, 10)$

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