IGNOU MTE 2 2018 - Check whether the vector (2,sqrt(3),3) sis equally inclined to t

Question

Check whether the vector (2,sqrt(3),3) sis equally inclined to the vectors (2,2 sqrt(3)) and (4,0).

02 Feb 2018

Answer :

Word Count : 376

To check whether the vector \( \mathbf{v} = (2, \sqrt{3}, 3) \) is equally inclined to the vectors \( \mathbf{a} = (2, 2\sqrt{3}) \) and \( \mathbf{b} = (4, 0) \), we need to use the concept of the dot product. Two vectors are equally inclined to a third vector if the angles between them are the same. The condition for two vectors to have the same angle with a third vector is that the dot product of the first vector with the second is equal to the dot product of the first vector with the third. ### Step 1: Dot product of \( \mathbf{v} \) with \( \mathbf{a} \) We first need to express the vectors \( \mathbf{a} \) and \( \mathbf{v} \) in 3D format by assuming a third component for \( \mathbf{a} \), which is 0

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