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Question

The vectors 3i^2j^+k^,i^3j^+5k^ and 2i^+j^4k^ form the sides of a triangle. This triangle is?


A

an equilateral triangle

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B

an isosceles triangle

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C

a right angled triangle

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D

collinear

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Solution

The correct option is C

a right angled triangle


Explanation for correct option

Let the three sides of triangle are AB,BC and AC

AB=2i^+j^-4k^BC=3i^2j^+k^AC=i^3j^+5k^|AB|=22+12+-42=4+1+16=21|BC|=32+-22+12=9+4+1=14|AC|=12+32+52=1+9+25=35

Now if we square all the three magnitudes, then we get;

|AB|2=21|BC|2=14|AC|2=35

As we can see,

|AB|2+|BC|2=|AC|221+14=35

The above condition is true for a right angled triangle

Hence option (C) is correct


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