Mathematics: If ⃗ = + + is perpendicular to both ⃗ = 5 + − 2 and = 3 − 3 + 6 , find and .

If ⃗ = + + is perpendicular to both ⃗ = 5 + − - id5213643879, larreanathalie3523

Ответ:

mikaelalcool49

06.07.2021

The values of and are 0 and 2, respectively.

Step-by-step explanation:

If $\vec {c} = m\,\hat{i} + n\,\hat{j} + \hat{k}$ is perpendicular to $\vec {a} = 5\,\hat{i} + \hat{j} -2\,\hat{k}$ and $\vec {b} = 3\,\hat{i} - 3\,\hat{j} + 6\,\hat{k}$ , then the following relationships must be observed:

$\vec {c}\,\bullet\,\vec {a} = 0$ (1)

$\vec{c}\,\bullet \,\vec{a} = 0$ (2)

Then, we expand the previous expressions:

$(m, n, 1)\,\bullet\,(5, 1, -2) = 0$

$5\cdot m + n = 2$ (1b)

$(m, n, 1)\,\bullet\,(3, -3, 6) = 0$

$3\cdot m - 3\cdot n = -6$ (2b)

Then, we solve for and :

m = 0, n = 2

The values of and are 0 and 2, respectively.

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Ответ:

AleOfficial101

23.04.2021

Mathematics

The correct answer is that AC = 4x - 2 or 2(2x - 1)

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

AD = 6x + 10

CD = 2x + 12

2. Let's find the length of AC

AC = AD - CD

Replacing with the real values:

AC = (6x + 10) - (2x + 12)

AC = 6x + 10 - 2x - 12

AC = 6x - 2x + 10 - 12

AC = 4x -2 or 2(2x - 1)

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If ⃗ = + + is perpendicular to both ⃗ = 5 + − 2 and = 3 − 3 + 6 , find and .

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