Find the angle between the vectors. (first find an exact expression and then approximate to the nearest degree.) a = 1, −4, 1 , b = 0, 3, −3

The angle between the two vectors given is of 146 degrees.

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In which

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Finding the angle:

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Using a calculator:

The angle between the two vectors is of 146 degrees.

A similar problem is given at link

The formula of the dot product of two vectors:

We have:

Calculate the dot product:

Calculate the lengths of vectors:

Substitute:

Measure of the angle between the vectors a and b is equal 146°.

x is variable or an unknown value to find

example:

2x = 5 which means x = 3