Q. 2 Equation of a plane: Find the eq... [FREE SOLUTION]

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Chapter 11: Q. 2 (page 879)

Equation of a plane: Find the equation of the plane determined by the vectors (1, 鈭�3, 5)and (2, 4, 鈭�1) and containing the point(0, 3, 鈭�2).

Short Answer

Expert verified

The equation of the plane is $- 17 x + 11 y + 10 z - 13 = 0 .$

Step by step solution

Step 1. Given Information.

The given vectors of the plane are (1, 鈭�3, 5)and (2, 4, 鈭�1)and the given containing point is(0, 3, 鈭�2).

Step 2. Finding the equation of a plane.

To find the equation of a plane determined by the vectors and containing the point, we will use the formula: $(\overset{鈫�}{r} - \overset{鈬赌}{a}) 路 (\overset{鈫�}{伪} 脳 \overset{鈫�}{尾}) = 0 .$

Let's find the cross product,

role="math" localid="1649641070012" $(\overset{鈫�}{伪} 脳 \overset{鈫�}{尾}) = |\begin{matrix} i & j & k \\ 1 & - 3 & 5 \\ 2 & 4 & - 1 \end{matrix}| = i ((- 3) (- 1) - (4) (5)) - j ((1) (- 1) - (2) (5)) + k ((1) (4) - (2) (- 3)) = - 17 i + 11 j + 10 k$

Now, let's do the difference,

role="math" localid="1649641452589" $(\overset{鈫�}{r} - \overset{鈫�}{a}) = (x i + y j + z k) - (0 i + 3 j - 2 k) = i (x - 0) + j (y - 3) + k (z - (- 2)) = x i + (y - 3) j + (z + 2) k$

Step 3. Calculate.

Now, let's do the dot product,

$[x i + (y - 3) j + (z + 2) k] 路 (- 17 i + 11 j + 10 k) = 0 (x) (- 17) + (y - 3) (11) + (z + 2) (10) = 0 - 17 x + 11 y - 33 + 10 z + 20 = 0 - 17 x + 11 y + 10 z - 13 = 0$

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91影视

Equation of a plane: Find the equation of the plane determined by the vectors (1, 鈭�3, 5)and (2, 4, 鈭�1) and containing the point(0, 3, 鈭�2).

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the equation of a plane.

Step 3. Calculate.

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