Question

If A, B, C are position vectors (2, 0, 0), (0, 1, 0) and (0, 0, 2) show that △ABC is isosceles .

Answer 1

Answer:

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Hope this helps.

Step-by-step explanation:

Check lengths of sides:

AB² = ( 2 - 0 )² + ( 0 - 1 )² + ( 0 - 0 )² = 4 + 1 = 5  =>  AB = √5

BC² = ( 0 - 0 )² + ( 1 - 0 )² + ( 0 - 2 )² = 1 + 4 = 5  =>  BC = √5

So the triangle is isosceles with AB = BC

(For completeness:

CA² = ( 0 - 2)² + ( 0 - 0 )² + ( 2 - 0 )² = 4 + 4 = 8  =>  CA = 2√2,

so the triangle is not equilateral.)

Answer 2

A=2,0,0
B=0,1,0
C=0,0,2

Isosceles triangle =A+B
=2+1
=3