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Question

$$\overset { - }{ A } =\overset { - }{ 2i }-\overset { - }{ j }+\overset { - }{ k },\overset { - }{ B }=\overset { - }{ i }-\overset { - }{ 3j }-\overset { - }{5k },\overset { - }{ C } =\overset { - }{ 3i }-\overset { - }{ 4j }-\overset { - }{ 4k }$$ are the vertices of a triangle.           


A
Scalene
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B
Equilateral
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C
Right angled
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D
Isosceles
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Solution

The correct option is C $$Right$$ $$angled$$
$$|AB|=\sqrt{(2-1)^2+(-1+3)^2+(1+5)2}$$
$$=\sqrt{1+4+36}=\sqrt{41}$$
$$|AC|=\sqrt{(2-3)^2+(-1+4)^2+(1+4)^2}$$
$$=\sqrt{1+9+25}$$
$$=\sqrt{35}$$
$$|BC|=\sqrt{(1-3)^2+(-3+4)^2+(-5+4)^2}$$
$$=\sqrt{4+1+1}$$
$$=\sqrt{6}$$
$$\therefore AB^2=AC^2+BC^2$$
$$41=35+6$$
$$41=41$$
$$\therefore$$ This is a right angle triangle.

1376742_1223993_ans_e20677497dc542769340db7663ac7765.PNG

Mathematics

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