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
B
Equilateral
C
Right angled
D
Isosceles

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.Mathematics

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