If the position vectors of the vertices of a triangle are A- - - - 2 - - 2 k- - B- - 2- - 3 - - k- - C- - 3 - - - - 2 k- - Check whether the triangle is equilateral or not-

A⃗=î+2̂ĵ+2̂k̂ B⃗=2̂î+3ĵ+k̂ C⃗=3̂î+ĵ 2̂k̂ A⃗B⃗=î+ĵ k̂=√(1^2+1^2+( 1)^2)=√(3) B⃗C⃗=î 2ĵ 3k̂=√(1^2+( 2)^2+( 3)^2)=√(14) C⃗A⃗=2î 1ĵ 4k ...

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Definition of Vector

If the positi...

Question

If the position vectors of the vertices of a triangle are $\to A =^i + 2^j + 2^k, \to B = 2^i + 3^j +^k, \to C = 3^i +^j - 2^k$ ; Check whether the triangle is equilateral or not.

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\to A =^i - 2^j + 2^k, \to B = 2^i +^j -^k

\to C = 3^i -^j + 2^k

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

\to a + 2 \to b - 3 \to c

\sqrt{78}

\to a = 3^i + 2^j + 2^k, \to b = -^i + 3^j -^k, \to c =^i +^j +^k

\to a \times (\to b \times \to c)

(\to a \times \to b) \times \to c

\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k

\to c = 3^i +^j + 2^k

\to a \cdot (\to b \times \to c)

\to a \cdot (\to b \times \to c)

\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k

\to c = 3^i +^j + 2^k .

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