# If #A = <2 ,2 ,5 >#, #B = <5 ,-7 ,8 ># and #C=A-B#, what is the angle between A and C?

The angle is

By signing up, you agree to our Terms of Service and Privacy Policy

The angle between vectors A and C can be found using the dot product formula. First, calculate vector C by subtracting vector B from vector A. Then, find the dot product of vectors A and C. Finally, use the dot product and the magnitudes of vectors A and C to calculate the angle between them using the formula:

[ \theta = \arccos\left(\frac{\mathbf{A} \cdot \mathbf{C}}{|\mathbf{A}| |\mathbf{C}|}\right) ]

Given vectors A and B, the components of vector C are obtained by subtracting the corresponding components of vector B from vector A:

[ C = A - B = \langle 2 - 5, 2 - (-7), 5 - 8 \rangle = \langle -3, 9, -3 \rangle ]

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

[ \mathbf{A} \cdot \mathbf{C} = (2 \cdot -3) + (2 \cdot 9) + (5 \cdot -3) = -6 + 18 - 15 = -3 ]

Then, find the magnitudes of vectors A and C:

[ |\mathbf{A}| = \sqrt{2^2 + 2^2 + 5^2} = \sqrt{4 + 4 + 25} = \sqrt{33} ] [ |\mathbf{C}| = \sqrt{(-3)^2 + 9^2 + (-3)^2} = \sqrt{9 + 81 + 9} = \sqrt{99} ]

Finally, substitute these values into the formula to find the angle:

[ \theta = \arccos\left(\frac{-3}{\sqrt{33} \cdot \sqrt{99}}\right) ] [ \theta \approx \arccos\left(\frac{-3}{\sqrt{3267}}\right) ] [ \theta \approx \arccos\left(-0.1624\right) ] [ \theta \approx 98.84^\circ ]

Therefore, the angle between vectors A and C is approximately (98.84^\circ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- In triangle ABC, if #a = 8.75# centimeters, #c = 4.26# centimeters, and #m/_B# is #87°# what is the length of #b# to two decimal places?
- A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #1#, respectively, and the angle between A and B is #(7pi)/8 #. What is the length of side C?
- Is (cotA+cotB)/(cotAcotB-1) equals to (cotAcotB-1)/(cotA+cotB) ?
- The sides of an isosceles triangle are 5, 5, and 7. How do you find the measure of the vertex angle to the nearest degree?
- What is the area of a triangle with sides of length 2, 4, and 5?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7