Find the direction cosine of the line x4 - y7 - z4

Looking at the given equation of the line, the line is parallel to 4î #160;+ 7ĵ + 4k̂ The direction cosines have to be such that they #160;should be co ...

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Standard XII

Mathematics

Direction Cosines

Find the dire...

Question

Find the direction cosine of the line $\frac{x}{4} = \frac{y}{7} = \frac{z}{4}$

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Solution

Looking at the given equation of the line, the line is parallel to $4^i + 7^j + 4^k$
The direction cosines have to be such that they should be components of a unit vector.
Dividing the direction ratio by its modulus, we have
$\frac{4^i + 7^j + 4^k}{\sqrt{4^{2} + 7^{2} + 4^{2}}}$
$= \frac{4^i + 7^j + 4^k}{\sqrt{81}}$
$= \frac{4^i + 7^j + 4^k}{9}$
The direction cosines thus can be written as $\frac{4}{9}, \frac{7}{9}, \frac{4}{9}$

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Find the direction cosine of the line x4=y7=z4

Find the direction cosine of the line $\frac{x}{4} = \frac{y}{7} = \frac{z}{4}$