7. Consider a general plane P with scalar equation ax + by + cz = d (a, b, c, d are constants). In this problem, we will investigate the distance between P and the origin O. Write down a vector parametrization T (t) for the line L that passes through the (a) origin O and is orthogonal to the plane P. Use t as the parameter. Your answer may include any of the constants a, b, c, d. (b) answer may include any of the constants a, b, c, d. Find the (position vector for the) point Q where this line L intersects P. Your (c) of the constants a, b, c, d. This distance is, by definition, the distance between P and O. Find the distance of the point Q from the origin O. Your answer may include any

7. Consider a general plane P with scalar equation ax + by + cz = d (a, b, c, d are constants). In this problem, we will investigate the distance between P and the origin O. Write down a vector parametrization T (t) for the line L that passes through the (a) origin O and is orthogonal to the plane P. Use t as the parameter. Your answer may include any of the constants a, b, c, d. (b) answer may include any of the constants a, b, c, d. Find the (position vector for the) point Q where this line L intersects P. Your (c) of the constants a, b, c, d. This distance is, by definition, the distance between P and O. Find the distance of the point Q from the origin O. Your answer may include any

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 47EQ

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