Answer:
hi just need points
Step-by-step explanation:
Answer with Step-by-step explanation:
We are given that
u+ v and u-v are orthogonal
We have to prove that u and v must have the same length.
When two vector a and b are orthogonal then
![a\cdot b=0](https://tex.z-dn.net/?f=a%5Ccdot%20b%3D0)
By using the property
![(u+v)\cdot (u-v)=0](https://tex.z-dn.net/?f=%28u%2Bv%29%5Ccdot%20%28u-v%29%3D0)
We know that
![(a+b)\cdot (a-b)=\mid a\mid^2-\mid b\mid^2](https://tex.z-dn.net/?f=%28a%2Bb%29%5Ccdot%20%28a-b%29%3D%5Cmid%20a%5Cmid%5E2-%5Cmid%20b%5Cmid%5E2)
![\mid u\mid ^2-\mid v\mid^2=0](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%20%5E2-%5Cmid%20v%5Cmid%5E2%3D0)
![\mid u\mid^2=\mid v\mid^2](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%5E2%3D%5Cmid%20v%5Cmid%5E2)
Magnitude is always positive
When power of base on both sides are equal then base will be equal
Therefore,
![\mid u\mid=\mid v\mid](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%3D%5Cmid%20v%5Cmid)
Hence, the length of vectors u and v must have the same length.
Answer:
Box A's volume is bigger by 864 cubic inches
Step-by-step explanation:
12 × 18 × 24 = 5184
12 × 12 × 30 = 4320
Then we subtract. 5184 - 4320 = 864
Answer:f ( x - 1 ) = 3x² - 5x - 7
Step-by-step explanation: