The direction cosines of the ray P(1, -2, 4) to Q(-1, 1, -2) are

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Question

The direction cosines of the ray P(1, -2, 4) to Q(-1, 1, -2) are

<-2, 3, -6>
<2, -3, 6>
\(\left\langle \frac{2}{7},-\frac{3}{7},\frac{6}{7} \right\rangle\)
\(\left\langle -\frac{2}{7},\frac{3}{7},-\frac{6}{7} \right\rangle\)

Answer 1

Concept:

Let \(\vec{A}\) be a vector with co-ordinates (x, y, z).

Then the direction cosines of vector \(\vec{A}\) are given by \(\left\langle \frac{x}{√{\left( {{x}^{2}}+{{y}^{2}}+{{z}^{2}} \right)}},~\frac{y}{√{\left( {{x}^{2}}+{{y}^{2}}+{{z}^{2}} \right)}},~\frac{z}{√{\left( {{x}^{2}}+{{y}^{2}}+{{z}^{2}} \right)}} \right\rangle \)

Calculation:

The co-ordinates of the vector \(\overrightarrow{PQ}\) is (-2, 3, -6).

Here x = -2, y = 3, z = -6.

√(x² + y² + z²) = √(4 + 9 + 36) = 7

∴ The direction cosines of the vector \(\overrightarrow{PQ}\) are: \(\left\langle \frac{-2}{7},\frac{3}{7},\frac{-6}{7} \right\rangle\)

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The direction cosines of the ray P(1, -2, 4) to Q(-1, 1, -2) are

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