5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b. Between the planes 2x – y + 5z = 0 and 2x – y + 5z = 5. c. From the point (1,2,3) to the line r = (-t, 4 – t,1+ 4t).

5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b. Between the planes 2x – y + 5z = 0 and 2x – y + 5z = 5. c. From the point (1,2,3) to the line r = (-t, 4 – t,1+ 4t).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 42EQ

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Question

5) Find the distances:
a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t).
%3D
b. Between the planes 2x – y + 5z = 0 and 2x – y + 5z = 5.
c. From the point (1,2,3) to the line r = (-t, 4 – t,1+ 4t).

Expert Solution

Step 1

Given:

(a). two lines l₁ and l₂

(b). Two Planes

(c). A point (1,2,3) and a line

To Find:

(a). Distance between two lines

(b). Distance between two planes.

(c). Distance between a point and a line.

Step 2

Explanation:

(a). As we have

let

Step 3

(b).

Here, we have

On Comparing we get

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