Question

find the angle btw i+j+k and i

Answer 1

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Answer 2

Answer:

arccos (1/√3).

Explanation:

We want to determine the angle between the vector i+j+k and the i which is X axis.

We can use the dot product to get this value.

The vector i is a unit vector along the X axis.

⇒ The angle between the vector i+j+k and the X axis is the same as the angle between the vector i+j+k and the vector i.

Let the angle between these two vectors by θ.

Taking the dot product of these two vectors, we get,

(i+j+k)⋅i = | i+j+k | | i |cosθ.

⇒1 =√3 ⋅1 ⋅cosθ ⇒ cosθ = 1/√3

⇒ θ = arccos (1/√3).

⇒ The angle between the vector i+j+k and the i or X axis is arccos (1/√3). (Answer)