Question

Question 4: If the direction cosines of a line are k/3,k/3,k/3, then value of k is
(a) k> 0
(b) 0 <k<1.
(c) k = 13
(d) k=73​

Answer 1

Direction Cosines

We must remember that if $l,m,n$ are the direction cosines of any straight line, then

• $l^{2}+m^{2}+n^{2}=1$

Step-by-step explanation:

Given that, the direction cosines of a line are $\frac{k}{3},\frac{k}{3},\frac{k}{3}$. Then

• $\quad (\frac{k}{3})^{2}+(\frac{k}{3})^{2}+(\frac{k}{3})^{2}=1$

• $\Rightarrow \frac{k^{2}}{9}+\frac{k^{2}}{9}+\frac{k^{2}}{9}=1$

• $\Rightarrow \frac{3k^{2}}{9}=1$

• $\Rightarrow k^{2}=3$

• $\Rightarrow k=\pm\sqrt{3}$

Answer:

Therefore the value of $k$ is $\pm\sqrt{3}$.

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find the direction cosine l,m,n of two lines which are connected by the relation l+m+n=0 and mn-2nl-2lm=0

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