Category:Components of Vector in terms of Direction Cosines

Let $\mathbf r$ be a vector quantity embedded in a Cartesian $3$-space.

Let $\mathbf i$, $\mathbf j$ and $\mathbf k$ be the unit vectors in the positive directions of the $x$-axis, $y$-axis and $z$-axis respectively.

Let $\cos \alpha$, $\cos \beta$ and $\cos \gamma$ be the direction cosines of $\mathbf r$ with respect to the $x$-axis, $y$-axis and $z$-axis respectively.

Let $x$, $y$ and $z$ be the components of $\mathbf r$ in the $\mathbf i$, $\mathbf j$ and $\mathbf k$ directions respectively.

Let $r$ denote the magnitude of $\mathbf r$, that is:

$r := \size {\mathbf r}$

Then:

$\ds x$

$=$

$\ds r \cos \alpha$

$\ds y$

$=$

$\ds r \cos \beta$

$\ds z$

$=$

$\ds r \cos \gamma$

Pages in category "Components of Vector in terms of Direction Cosines"

The following 2 pages are in this category, out of 2 total.