Direction cosines

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What do the direction cosines $(\cos\alpha,\cos\beta,\cos\gamma)$ of a vector represent?

A.The cosines of the angles the vector makes with the positive

x

y

, and

z

axes respectively

B.The components of the vector itself, unscaled

C.The sines of the angles the vector makes with the coordinate planes

D.The ratios of the vector's components to its largest component

Find the direction cosines of $\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}$ .

\left(\dfrac{1}{3},\dfrac{2}{3},\dfrac{2}{3}\right)

\left(\dfrac{1}{9},\dfrac{2}{9},\dfrac{2}{9}\right)

(1,2,2)

\left(\dfrac{2}{3},\dfrac{1}{3},\dfrac{2}{3}\right)

Find the direction cosines of $\mathbf{a}=4\mathbf{i}+4\mathbf{j}+7\mathbf{k}$ .

\left(\dfrac{4}{9},\dfrac{4}{9},\dfrac{7}{9}\right)

\left(\dfrac{4}{81},\dfrac{4}{81},\dfrac{7}{81}\right)

(4,4,7)

\left(\dfrac{7}{9},\dfrac{4}{9},\dfrac{4}{9}\right)

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