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Question

# Vectors →a=(3^i−2^j+^k), →b=(^i−3^j+5^k) and →c=(2^i+^j−4^k) have a characteristics to form

A
equilateral triangle
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B
isosceles triangle
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C
right angled triangle
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D
scalene triangle
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Solution

## The correct option is C right angled triangle Here, →b+→c=(^i−3^j+5^k)+(2^i+^j−4^k) =3^i−2^j+^k ⇒→b+→c=→a ∴→a,→b,→c represent sides of a triangle. |→a|=√(3)2+(−2)2+(1)2 =√9+4+1 =√14 |→b|=√(1)2+(−3)2+(5)2 =√1+9+25 ⇒|→b|=√35 |→c|=√(2)2+(1)2+(−4)2 =√4+1+16 =√21 ⇒(√21)2+(√14)2=(√35)2 ⇒21+14=35 35=35 ⟹|→c|2+|→a|2=|→b|2 By the Pythagoras theorem, triangle formed by →a, →band →c is a right angled triangle

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