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  • Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

Q.13  Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

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best_answer

Given 

point A=(1, 2, –3)

point B=(–1, –2, 1)

Vector joining A and B Directed from A to B

\vec {AB}=(-1-1)\hat i +(-2-2)\hat j+(1-(-3))\hat k

\vec {AB}=-2\hat i +-4\hat j+4\hat k

\left | \vec {AB} \right |=\sqrt{(-2)^2+(-4)^2+4^2}=\sqrt{36}=6

Hence Direction cosines of vector AB are

\left ( \frac{-2}{6},\frac{-4}{6},\frac{4}{6} \right )=\left ( \frac{-1}{3},\frac{-2}{3},\frac{2}{3} \right )

 

Posted by

Pankaj Sanodiya

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