Explanation Given: The line passes through the point ( 2 , 3 , 4 ) and is parallel to the x z -plane and y z -plane. Formula used: The parametric equations of a line are: x = x 1 + a t , y = y 1 + b t and z = z 1 + c t . Cross product of two vectors : n 1 × n 2 = | i j k a 1 a 2 a 3 b 1 b 2 b 3 | Calculation: Cross product of two vector quantities results in a mutually perpendicular third quantity. Therefore, the cross product of the normal vectors of both the planes will be a parallel vector to the line. Then normal vector of x z -plane will be in y direction. As we know the given line is parallel to both x z -plane and y z -plane, Implies, that the line is perpendicular to the normal vector of both the planes. n 1 = 〈 0 , 1 , 0 〉 . Further the normal vector of y z -plane will be in x direction. then, n 2 = 〈 1 , 0 , 0 〉 . Further let us find the cross product of two vectors: n 1 × n 2 = | i j k a 1 a 2 a 3 b 1 b 2 b 3 | Again substituting the values And only then find cross product of two vectors, n 1 × n 2 = | i j k 0 1 0 1 0 0 | = | 1 0 0

11th Edition

ISBN: 9781337604796

Author: Larson

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 11.5, Problem 17E

To determine

To calculate: Find Set of parametric equations of a line passing through the

point (2,3,4) and is parallel to the xz-plane and yz-plane

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 16E

Chapter 11.5, Problem 18E

Students have asked these similar questions

The parametric equations of the function are given asx=asin²0, y = acos). Calculate [Let: a=anumerical coefficient] dy d²y and dx dx2

A tank contains 200 gal of fresh water. A solution containing 4 lb/gal of soluble lawn fertilizer runs into the tank at the rate of 1 gal/min, and the mixture is pumped out of the tank at the rate of 5 gal/min. Find the maximum amount of fertilizer in the tank and the time required to reach the maximum. Find the time required to reach the maximum amount of fertilizer in the tank. t= min (Type an integer or decimal rounded to the nearest tenth as needed.)

Thumbi Irrigation Scheme in Mzimba district is under threat of flooding. In order to mitigate against the problem, authorities have decided to construct a flood protection bund (Dyke). Figure 1 is a cross section of a 300m long proposed dyke; together with its foundation (key). Survey data for the proposed site of the dyke are presented in Table 1. Table 2 provides swelling and shrinkage factors for the fill material that has been proposed. The dyke dimensions that are given are for a compacted fill. (1) Assume you are in the design office, use both the Simpson Rule and Trapezoidal Rule to compute the total volume of earthworks required. (Assume both the dyke and the key will use the same material). (2) If you are a Contractor, how many days will it take to finish hauling the computed earthworks using 3 tippers of 12m³ each? Make appropriate assumptions. DIKE CROSS SECTION OGL KEY (FOUNDATION) 2m 1m 2m 8m Figure 1: Cross section of Dyke and its foundation 1.5m from highest OGL 0.5m…

Chapter 11 Solutions

Multivariable Calculus - With WebAssign

Ch. 11.1 - CONCEPT CHECK Scalar and Vector Describe the...Ch. 11.1 - CONCEPT CHECK Vector Two points and a vector are...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Prob. 4E Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find Set of parametric equations of a line passing through the point ( 2 , 3 , 4 ) and is parallel to the x z -plane and y z -plane

Solution Summary: The author explains the parametric equations of a line passing through the point (2,3,4) and is parallel to the xz -plane and yz

Concept explainers

To calculate: Find Set of parametric equations of a line passing through the

point (2,3,4) and is parallel to the xz-plane and yz-plane

Want to see the full answer?

Chapter 11 Solutions

Find Set of parametric equations of a line passing through the point ( 2 , 3 , 4 ) and is parallel to the x z -plane and y z -plane

Solution Summary: The author explains the parametric equations of a line passing through the point (2,3,4) and is parallel to the xz -plane and yz

Concept explainers

To calculate: Find Set of parametric equations of a line passing through the point (2,3,4) and is parallel to the xz-plane and yz-plane

Want to see the full answer?

Chapter 11 Solutions

To calculate: Find Set of parametric equations of a line passing through the

point (2,3,4) and is parallel to the xz-plane and yz-plane