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Q16  Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.

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A=(1, 2, 7), B=(2, 6, 3) and C(3, 10, –1)

To show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear

\vec {AB}=(2-1)\hat i+(6-2)\hat j+(3-7)\hat k

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

\vec {BC}=(3-2)\hat i+(10-6)\hat j+(-1-3)\hat k

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

\vec {AC}=(3-1)\hat i+(10-2)\hat j+(-1-7)\hat k

\vec {AC}=2\hat i+8\hat j-8\hat k

|\vec {AB}|=\sqrt{1^2+4^2+(-4)^2}=\sqrt{33}

|\vec {BC}|=\sqrt{1^2+4^2+(-4)^2}=\sqrt{33}

|\vec {AC}|=\sqrt{2^2+8^2+(-8)^2}=2\sqrt{33}

As we see that 

|\vec {AC}|=|\vec {AB}|+|\vec {BC}|

Hence point A, B , and C are colinear.

Posted by

Pankaj Sanodiya

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