Answer:
What ever the length and width is you times them both I don't know if you exactly know that are now but I think it is C
Hope it helps have a great day:)
Answer:
(2,9)
Step-by-step explanation:
Answer:
it would be 140
Step-by-step explanation:
Given
![\vec{a}=2\vec{i}-\vec{j}+5\vec{k},](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%3D2%5Cvec%7Bi%7D-%5Cvec%7Bj%7D%2B5%5Cvec%7Bk%7D%2C)
![\vec{b}=\vec{i}+2\vec{j}+4\vec{k},](https://tex.z-dn.net/?f=%5Cvec%7Bb%7D%3D%5Cvec%7Bi%7D%2B2%5Cvec%7Bj%7D%2B4%5Cvec%7Bk%7D%2C)
you can find
![\vec{a}-\vec{b}=2\vec{i}-\vec{j}+5\vec{k}-(\vec{i}+2\vec{j}+4\vec{k})=\vec{i}-3\vec{j}+\vec{k}.](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D-%5Cvec%7Bb%7D%3D2%5Cvec%7Bi%7D-%5Cvec%7Bj%7D%2B5%5Cvec%7Bk%7D-%28%5Cvec%7Bi%7D%2B2%5Cvec%7Bj%7D%2B4%5Cvec%7Bk%7D%29%3D%5Cvec%7Bi%7D-3%5Cvec%7Bj%7D%2B%5Cvec%7Bk%7D.)
Three vectors
form a triangle.
1.
![\cos\angle 1=\dfrac{\vec{a}\cdot \vec{b}}{|\vec{a}|\cdot |\vec{b}|}=\dfrac{2\cdot 1+(-1)\cdot 2+5\cdot 4}{\sqrt{2^2+(-1)^2+5^2}\cdot \sqrt{1^2+2^2+4^2} }=\dfrac{20}{\sqrt{30} \cdot \sqrt{21} }.](https://tex.z-dn.net/?f=%5Ccos%5Cangle%201%3D%5Cdfrac%7B%5Cvec%7Ba%7D%5Ccdot%20%5Cvec%7Bb%7D%7D%7B%7C%5Cvec%7Ba%7D%7C%5Ccdot%20%7C%5Cvec%7Bb%7D%7C%7D%3D%5Cdfrac%7B2%5Ccdot%201%2B%28-1%29%5Ccdot%202%2B5%5Ccdot%204%7D%7B%5Csqrt%7B2%5E2%2B%28-1%29%5E2%2B5%5E2%7D%5Ccdot%20%5Csqrt%7B1%5E2%2B2%5E2%2B4%5E2%7D%20%7D%3D%5Cdfrac%7B20%7D%7B%5Csqrt%7B30%7D%20%5Ccdot%20%5Csqrt%7B21%7D%20%7D.)
2.
![\cos\angle 2=\dfrac{\vec{a}\cdot (\vec{a}-\vec{b})}{|\vec{a}|\cdot |\vec{a}-\vec{b}|}=\dfrac{2\cdot 1+(-1)\cdot (-3)+5\cdot 1}{\sqrt{2^2+(-1)^2+5^2}\cdot \sqrt{1^2+(-3)^2+1^2} }=\dfrac{10}{\sqrt{30} \cdot \sqrt{11} }.](https://tex.z-dn.net/?f=%5Ccos%5Cangle%202%3D%5Cdfrac%7B%5Cvec%7Ba%7D%5Ccdot%20%28%5Cvec%7Ba%7D-%5Cvec%7Bb%7D%29%7D%7B%7C%5Cvec%7Ba%7D%7C%5Ccdot%20%7C%5Cvec%7Ba%7D-%5Cvec%7Bb%7D%7C%7D%3D%5Cdfrac%7B2%5Ccdot%201%2B%28-1%29%5Ccdot%20%28-3%29%2B5%5Ccdot%201%7D%7B%5Csqrt%7B2%5E2%2B%28-1%29%5E2%2B5%5E2%7D%5Ccdot%20%5Csqrt%7B1%5E2%2B%28-3%29%5E2%2B1%5E2%7D%20%7D%3D%5Cdfrac%7B10%7D%7B%5Csqrt%7B30%7D%20%5Ccdot%20%5Csqrt%7B11%7D%20%7D.)
3.
![\cos\angle 3=\dfrac{\vec{b}\cdot (\vec{a}-\vec{b})}{|\vec{b}|\cdot |\vec{a}-\vec{b}|}=\dfrac{1\cdot 1+2\cdot (-3)+4\cdot 1}{\sqrt{1^2+2^2+4^2}\cdot \sqrt{1^2+(-3)^2+1^2} }=\dfrac{-1}{\sqrt{21} \cdot \sqrt{11} }.](https://tex.z-dn.net/?f=%5Ccos%5Cangle%203%3D%5Cdfrac%7B%5Cvec%7Bb%7D%5Ccdot%20%28%5Cvec%7Ba%7D-%5Cvec%7Bb%7D%29%7D%7B%7C%5Cvec%7Bb%7D%7C%5Ccdot%20%7C%5Cvec%7Ba%7D-%5Cvec%7Bb%7D%7C%7D%3D%5Cdfrac%7B1%5Ccdot%201%2B2%5Ccdot%20%28-3%29%2B4%5Ccdot%201%7D%7B%5Csqrt%7B1%5E2%2B2%5E2%2B4%5E2%7D%5Ccdot%20%5Csqrt%7B1%5E2%2B%28-3%29%5E2%2B1%5E2%7D%20%7D%3D%5Cdfrac%7B-1%7D%7B%5Csqrt%7B21%7D%20%5Ccdot%20%5Csqrt%7B11%7D%20%7D.)
Then