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Vector Addition

Let a, β ,γ...

Question

Let a, $β, γ$ be distinct real numbers. The points with position vectors ai + $β j + γ k, β i + γ j + a k, γ i + a j + β k .$

A

are collinear

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B

form an equilateral triangle

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C

form an scalene triangle

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D

form a right angled triangle

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Solution

The correct option is C form an equilateral triangle
$∣ ∣ ∣ - - \to A B ∣ ∣ ∣ = {[{(α - β)}^{2} + {(β - y)}^{2} + {(y - α)}^{2}]}^{\frac{1}{2}}$
$∣ ∣ ∣ - - \to B C ∣ ∣ ∣ = {[{(β - y)}^{2} + {(y - α)}^{2} + {(α - β)}^{2}]}^{\frac{1}{2}}$
$∣ ∣ ∣ - - \to C A ∣ ∣ ∣ = {[{(α - y)}^{2} + {(β - α)}^{2} + {(y - β)}^{2}]}^{\frac{1}{2}}$

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