Projection of a vector on $3$ coordinate axes are $6, - 3, 2$ respectively. Then DC's of vector are-

6, - 3, 2

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\frac{6}{5}, \frac{- 3}{5}, \frac{2}{5}

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\frac{- 6}{7}, \frac{- 3}{2}, \frac{2}{7}

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\frac{6}{7}, \frac{- 3}{7}, \frac{2}{7}

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Solution

The correct option is D $\frac{6}{7}, \frac{- 3}{7}, \frac{2}{7}$
Projection of a vector on coordinate axis are $X_{2} - X_{1}, Y_{2} - Y_{1}, Z_{2} - Z_{1}$
$X_{2} - X_{1} = 6, Y_{2} - Y_{1} = - 3, Z_{2} - Z_{1} = 2$
$\sqrt{{(X_{2} - X_{1})}^{2} + {(Y_{2} - Y_{1})}^{2} + {(Z_{2} - Z_{1})}^{2}} = \sqrt{36 + 9 + 4} = 7$
The Direction cosines of the vector are $\frac{6}{7}, \frac{- 3}{7}, \frac{2}{7}$

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Projection of a vector on 3 coordinate axes are 6,−3,2 respectively. Then DC's of vector are-

The correct option is D 67,−37,27Projection of a vector on coordinate axis are X2−X1,Y2−Y1,Z2−Z1 X2−X1=6,Y2−Y1=−3,Z2−Z1=2√(X2−X1)2+(Y2−Y1)2+(Z2−Z1)2=√36+9+4=7The Direction cosines of the vector are 67,−37,27

Projection of a vector on $3$ coordinate axes are $6, - 3, 2$ respectively. Then DC's of vector are-