Answer:
The angle between the two vectors is 84.813°.
Step-by-step explanation:
Statement is incomplete. Complete form is presented below:
<em>Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors. </em>
Let
and
, the angle between the two vectors is determined from definition of dot product:
(1)
Where:
,
- Vectors.
,
- Norms of each vector.
Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.
If we know that
and
, then the angle between the two vectors is:
![\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right]](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%286%29%5Ccdot%20%288%29%20%2B%20%28-3%29%5Ccdot%20%289%29%20%2B%20%281%29%5Ccdot%20%28-11%29%7D%7B%5Csqrt%7B6%5E%7B2%7D%2B%28-3%29%5E%7B2%7D%2B1%5E%7B2%7D%7D%5Ccdot%20%5Csqrt%7B8%5E%7B2%7D%2B9%5E%7B2%7D%2B%28-11%29%5E%7B2%7D%7D%7D%20%5Cright%5D)

The angle between the two vectors is 84.813°.
Answer:
1 movie ticket costs $9. I hope this helps!
Step-by-step explanation:
Answer: b
Step-by-step explanation:
There is 7,000 female students, and 5,000 male students. Because, if there was 2,000 more female students then male, you have to find out what two numbers add up to 12,000. (Tip, to make it easier, take away the thousands, like 7+5)