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2 Express the following planes in vector form (a) ?1 ? ?³ with equation 4x – z = 0. (b) ?? ? ?³ which passes through the points A = (-1, -1, 0), B = (2, 3, 5), and C = (3, 3, 3). (c) ?? ? ?³ with equation 4x – 3y + z = -10. (d) ?? ? ?³ which is parallel to the yz-plane but passes through the point X = (1, -1, 1). (e) ?². (f) ?? ? ?? which passes through A = (1, -1, 1, -1), and where the coordinates of every point in ?? satisfy the equations x + y + 2z – w = 3 and x + y + z + w = 0.

          2 Express the following planes in vector form
(a) ?1 ? ?³ with equation 4x – z = 0.
(b) ?? ? ?³ which passes through the points A = (-1, -1, 0), B = (2, 3, 5), and C = (3, 3, 3).
(c) ?? ? ?³ with equation 4x – 3y + z = -10.
(d) ?? ? ?³ which is parallel to the yz-plane but passes through the point X = (1, -1, 1).
(e) ?².
(f) ?? ? ?? which passes through A = (1, -1, 1, -1), and where the coordinates of every point in ?? satisfy the equations x + y + 2z – w = 3 and x + y + z + w = 0.

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2 Express the following planes in vector form
(a) ?1 ? ?³ with equation 4x – z = 0.
(b) ?? ? ?³ which passes through the points A = (-1, -1, 0), B = (2, 3, 5), and C = (3, 3, 3).
(c) ?? ? ?³ with equation 4x – 3y + z = -10.
(d) ?? ? ?³ which is parallel to the yz-plane but passes through the point X = (1, -1, 1).
(e) ?².
(f) ?? ? ?? which passes through A = (1, -1, 1, -1), and where the coordinates of every point in ?? satisfy the equations x + y + 2z – w = 3 and x + y + z + w = 0.

Added by Samantha G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/12/2023

Step 1

The normal vector of the plane is given by the coefficients of x, y, and z, which is (4, 0, -1). So, the vector form of the plane is: $$\boldsymbol{n} \cdot (\boldsymbol{r} - \boldsymbol{r_0}) = 0$$ where $\boldsymbol{n} = (4, 0, -1)$ is the normal vector, Show more…

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2 Express the following planes in vector form (a) P1 ⊆ R3 with equation 4x - z = 0. (b) P2 ⊆ R3 which passes through the points A = (-1,-1,0), B = (2, 3, 5), and C = (3,3,3). (c) P3 ⊆ R3 with equation 4x - 3y + z = -10. (d) P4 ⊆ R3 which is parallel to the yz-plane but passes through the point X = (1,-1,1). (e) R2. (f) P5 ⊆ R4 which passes through A = (1,-1, 1,-1), and where the coordinates of every point in P5 satisfy the equations x + y + 2z - w = 3 and x + y + z + w = 0.

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