# The equation 2x1 3x2 6x3 = 4 defines a plane in R3. a. Give its normal vector a. b. Find

Chapter 1, Problem 8

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QUESTION:

The equation $$2 x_{1}-3 x_{2}-6 x_{3}=-4$$ defines a plane in $$\mathbb{R}^{3}$$.

a. Give its normal vector a.

b. Find the distance from the origin to the plane by using projection.

c. Find the point on the plane closest to the origin by using the parametric equation of the line through $$0$$ with direction vector a. Double-check your answer to part b.

d. Find the distance from the point $$\mathbf{w}=(3,-3,-5)$$ to the plane by using projection.

e. Find the point on the plane closest to w by using the parametric equation of the line through w with direction vector a. Double-check your answer to part d.

### Questions & Answers (3 Reviews)

QUESTION:

The equation $$2 x_{1}-3 x_{2}-6 x_{3}=-4$$ defines a plane in $$\mathbb{R}^{3}$$.

a. Give its normal vector a.

b. Find the distance from the origin to the plane by using projection.

c. Find the point on the plane closest to the origin by using the parametric equation of the line through $$0$$ with direction vector a. Double-check your answer to part b.

d. Find the distance from the point $$\mathbf{w}=(3,-3,-5)$$ to the plane by using projection.

e. Find the point on the plane closest to w by using the parametric equation of the line through w with direction vector a. Double-check your answer to part d.

ANSWER:

Step 1 of 9

Given plane: $$2{x_1} - 3{x_2} - 6{x_3} = - 4$$ in $$\text{R}^3$$.

### Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

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### Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

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Textbook: Linear Algebra: A Geometric Approach

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### Review this written solution for 964057) viewed: 340 isbn: 9781429215213 | Linear Algebra: A Geometric Approach - 2 Edition - Chapter 1.3 - Problem 8

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Textbook: Linear Algebra: A Geometric Approach

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