show that a vector = 3i-2j+k,b vector=i-3j+5k,c vector=2i+j-4k form a right angle triangle
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We have a=(3
i
^
−2
j
^
+
k
^
) , b=(
i
^
−3
j
^
−4
k
^
) and c=(2
i
^
+
j
^
−4
k
^
)
Since b+c=a ⇒ (
i
^
−3
j
^
−4
k
^
) +(2
i
^
+
j
^
−4
k
^
) =(3
i
^
−2
j
^
+
k
^
)
so, a, b and c formed a triangle.
Also,
a
.
c
= (3
i
^
−2
j
^
+
k
^
) .(2
i
^
+
j
^
−4
k
^
)=(+6−2−4)=0
So,
a
and
c
are perpendicular.
Therefore, a,bandc form a right angled triangle.
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