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3 years ago

Find a normal vector n to the plane z−5(x−2)=2(8−y)

Mathematics

1 answer:

Hitman42 [59]3 years ago

7 0

A normal vector is the set of coefficients of x, y, and z when the equation is written in standard (or general) form.

Subtracting the left side, we have

... 2(8 -y) -z +5(x -2) = 0

... 16 -2y -z +5x -10 = 0

... 5x -2y -z +6 = 0 . . . . . general form

A normal vector is (5, -2, -1).

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3 years ago

Expand and simply <br>a) 2(4c+5d)+3(c-3d) <br>b) 6(3m+n)-4(m-n)<br>

dezoksy [38]

Answer:

a. 11x + d

b. 15m + 10n

Step-by-step explanation:

a. 2(4c+5d) + 3(x-3d)

Break the brackets:

2*4c + 2*5d + 3*x - 3*3d

= 8x + 10d + 3x - 9d

Collect like termsL

= 8x + 3x + 10d - 9d

= 11x + 1d

b. 6(3m+n) - 4(m-n)

Break the brackets:

= 6*3m + 6*n - 3*m - 4*(-n)

= 18m + 6n - 3m - (-4n)

= 18m -3m + 6n + 4n

= 15m + 10n

Hope this helped :3

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3 years ago