# If #A = <1 ,6 ,9 >#, #B = <-9 ,4 ,-8 ># and #C=A-B#, what is the angle between A and C?

The angle is

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To find the angle between two vectors A and C, you can use the dot product formula:

( \text{cos}(\theta) = \frac{{A \cdot C}}{{|A||C|}} )

Where:

- ( A \cdot C ) is the dot product of vectors A and C.
- ( |A| ) and ( |C| ) are the magnitudes of vectors A and C respectively.

First, calculate the dot product of vectors A and C:

( A \cdot C = (1)(1) + (6)(-9) + (9)(-8) )

Then, find the magnitudes of vectors A and C:

( |A| = \sqrt{1^2 + 6^2 + 9^2} ) ( |C| = \sqrt{(1 - (-9))^2 + (6 - 4)^2 + (9 - (-8))^2} )

Finally, substitute the values into the formula to find the angle ( \theta ) between A and C:

( \text{cos}(\theta) = \frac{{A \cdot C}}{{|A||C|}} )

( \theta = \text{cos}^{-1}\left(\frac{{A \cdot C}}{{|A||C|}}\right) )

Calculate the value of ( \theta ) using the arccosine function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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