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:
x = 
Step-by-step explanation:
Given 2 intersecting chords, then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
18x = 9 × 3 = 27 ( divide both sides by 18 )
x = 
=
In mathematical logic, the Law of Syllogism says that if the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r . Let p be the statement " you miss the bus", let q be the statement "you will be late to school", and let r be the statement "you will get detention". Then (1) and (2) can be written 1) If p , then q . 2) If q , then r . So, by the Law of Syllogism, we can deduce 3) If p , then r or If you miss the bus then you will get detention
