a=3i+4j+5k, b=I-j-2k, c=2i-3j-3kthen a+b+c=
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Answer:
Let OA=2i+4j−k,OB=4i+5j+k
and Oc=3i+6j−3k
Now, AB=OB−OA=2i+j+2k
∴AB=∣2i+j+2k∣=
4+1+4
=
9
=3
BC=OC−OB=−i+j−4k
∴BC=∣−i+j−4k∣=
1+1+16
=
18
=3
2
and CA=OA−OC=−i−2j+2k
∴CA=∣−i−2j+2k∣=
1+4+4
=
9
=3
Now, BC
2
=AB
2
+CA
2
(by Pythagoras theorem)
⇒(3
2
)
2
=(3)
2
+(3)
2
⇒18=18
So, triangle is isosceles right angled triangle.
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