a vector is represented by 2i + 3 j + 4 k than the cost of angle made by the vector with y axis
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Okay, so we know that A = 2i + 3j.
If we wish to find the angle between A and the y-axis, we can use any vector that only has a y-component. It is easiest to use the unit vector in the y-direction which is denoted by y= 1j.
To calculate the angle between the two vectors, we only need to manipulate the dot product equation. We know that a•b=|a||b|cos(θ) where θ is the angle between the two vectors. We can rearrange and get arccos[(a•b)/(|a||b|)] = θ.
After plugging in the values and computing both the dot product and magnitudes, we find that θ is roughly equal to 33.7 degrees.
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