Question

Is the triangle formed by the vectors 3i + 5j + 2k, 2i - 3j - 5k and -5i - 2j+ 3k equilateral?

Answer 1

Answer: YES, the triangle is Equilateral.

The given vector are

3i + 5j + 2k    ,     2i - 3j - 5k     and    -5i - 2j+ 3k

The magnitudes of these vectors will represent the sides of the triangle.

Equilateral triangle has all sides equal in length.

Now

$MagnitudeOfVector1=\sqrt{(3)^{2}+(5)^{2}+(2)^{2}}=\sqrt{38}\\ MagnitudeOfVector2=\sqrt{(2)^{2}+(-3)^{2}+(-5)^{2}}=\sqrt{38}\\ MagnitudeOfVector3=\sqrt{(-5)^{2}+(-2)^{2}+(3)^{2}}=\sqrt{38}$

Magnitudes of all three vectors is same.

So the sides of Triangles are equal in length.

So the triangle is Equilateral.

Answer 2

Answer:

Hence , it forms an equi lateral tri angle