Answer:
Therefore the given vectors are orthogonal for b = 0,±3.
Step-by-step explanation:
If
and
are two vectors orthogonal, then the dot product of
and
will be zero.
i.e ![\vec a. \vec b =0](https://tex.z-dn.net/?f=%5Cvec%20a.%20%5Cvec%20b%20%3D0)
If
and ![\vec b = x_2\hat i+y_2\hat j +z_2\hat k](https://tex.z-dn.net/?f=%5Cvec%20b%20%3D%20x_2%5Chat%20i%2By_2%5Chat%20j%20%2Bz_2%5Chat%20k)
![\vec a. \vec b=( x_1\hat i+y_1\hat j +z_1\hat k).( x_2\hat i+y_2\hat j +z_2\hat k)](https://tex.z-dn.net/?f=%5Cvec%20a.%20%5Cvec%20b%3D%28%20x_1%5Chat%20i%2By_1%5Chat%20j%20%2Bz_1%5Chat%20k%29.%28%20x_2%5Chat%20i%2By_2%5Chat%20j%20%2Bz_2%5Chat%20k%29)
![=x_1 x_2+y_1y_2+z_1z_2](https://tex.z-dn.net/?f=%3Dx_1%20x_2%2By_1y_2%2Bz_1z_2)
Given two vectors are (-18,b,9) and (b,b²,b)
Let
![\vec P= -18 \hat i+b\hat j +9 \hat k](https://tex.z-dn.net/?f=%5Cvec%20P%3D%20-18%20%5Chat%20i%2Bb%5Chat%20j%20%2B9%20%5Chat%20k)
and
![\vec Q = b \hat i+b^2 \hat j +b\hat k](https://tex.z-dn.net/?f=%5Cvec%20Q%20%3D%20b%20%5Chat%20i%2Bb%5E2%20%5Chat%20j%20%2Bb%5Chat%20k)
Therefore,
![\vec P.\vec Q](https://tex.z-dn.net/?f=%5Cvec%20P.%5Cvec%20Q)
![=( -18 \hat i+b\hat j +9 \hat k).( b \hat i+b^2 \hat j +b\hat k)](https://tex.z-dn.net/?f=%3D%28%20-18%20%5Chat%20i%2Bb%5Chat%20j%20%2B9%20%5Chat%20k%29.%28%20b%20%5Chat%20i%2Bb%5E2%20%5Chat%20j%20%2Bb%5Chat%20k%29)
=(-18).b+b.b²+9.b
= -18b+b³+9b
= b³-9b
Since
and
are orthogonal. Then
= 0.
Therefore,
b³-9b= 0
⇒b(b²-9)=0
⇒b =0 or b²=9
⇒b=0 or b =±3
Therefore the given vectors are orthogonal for b = 0,±3.
Answer:
i think so what is aap name
The total cost of 1000 CD's given that each costs $6.45 is equal to $6450. The revenue is the product of the number of CD's sold, n, and the selling price of each is $12.95. The equation for the profit or loss of "CD Universe" is, P = 12.95n - 6450
Answer:
\/
Step-by-step explanation:
Let x = number of half-gallons the store bought
(x-15) is the number of half-gallons the store sold
Profit = Income - Cost
$65.72 = (x-15)*3.96 - (x)2.60
65.72= 3.96x - 59.40 - 2.60x [distribute]
125.12 = 1.36x [collect terms]
92 = x