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Applications of Dot Product

If the vector...

Question

If the vectors 6i - 2j +3k , 2i +3j -6k and 3i + 6j -2k form a triangle, then it is

Right angled

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Equilateral

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Obtuse angled

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Isosceles

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Solution

The correct option is B Equilateral
Consider the problem
let the vector given are,
$a = 6^i - 2^j + 3^k$
$b = 2^i + 3^j - 6^k$
$c = 3^i + 6^j - 2^k$
now magnitude,
$| a | = \sqrt{6^{2} + 2^{2} + 3^{2}} = \sqrt{49} = 7$
Similarly, $b = 7$ and $c = 7$
Therefore, the triangle formed by these vectors is Equilateral.

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