Tutorial ExerciseThe vector A has x, y, and z components of 2.00, -5.00, and 0.99 units, respectively.(a) Write a vector expression for A in unit-vector notation.(b) Obtain a unit-vector expression for a vector B one-fourth the length of A pointing in the same direction as A.Step 3(c) Obtain a unit-vector expression for a vector C three times the length of A pointing in the direction oppositethe direction of A.Step 1Let's visualize the vectors in three dimensions. We begin by using cm as our unit of length. Look at the axes in thefigure. Let the edge of your desk be the x axis with unit vector î in the positive x direction. The positive z axis with unitvector k points toward you. Unit vector ĵ points up vertically from your desk in the positive y direction. Hold yourfingertip at the center of the front edge of your desk; this point will be the origin of our desk-based three-dimensionalcoordinate system. Move your finger 2.00 cm to the right, then -5.00 cm vertically up, and then -0.99 cm horizontallyaway from you. This location relative to the starting point roughly represents position vector A. Move three fourths ofthe way back toward the origin along A. Now the position of your fingertip relative to the origin roughly representsposition vector B. To approximate position vector C, move your finger in the opposite direction of A, for three times thelength of A, from the origin. Relative to the origin, or starting point on your desk, this approximates the position vectorč.Step 2We use unit-vector notation throughout. We will perform scalar multiplication on vector A to form vectors B and C. Forour desktop demonstration, we used cm as a convenient unit, but no specific units are given in this problem.(a) A = A¸î + A₁Ĵ+AK A =(b) B=Ā4(c) C = -3AB =QčHow do we find the magnitude of a three-dimensional vector? We apply the Pythagorean Theorem in three dimensions.The magnitude of vector A, for example, is given by A = √√A₂² + A, ². + A₂². You can see that multiplying a vector bya scalar multiplies the magnitude of the resulting vector by the absolute value of the scalar, for example,C = 3v Ax + Av+ A₂² = 3A.

Answered: Image /qna-images/answer/2ed6e2e4-f27e-45af-a35b-66f315798dd1.jpg

The vector A has x, y, and z components of 2.00, -5.00, and 0.99 units, respectively. (a) Write a vector expression for A in unit-vector notation. (b) Obtain a unit-vector expression for a vector B one-fourth the length of A pointing in the same direction as A (c) Obtain a unit-vector expression for a vector C three times the length of A pointing in the direction opposite the direction of A

The vector A has x, y, and z components of 2.00, -5.00, and 0.99 units, respectively. (a) Write a vector expression for A in unit-vector notation. (b) Obtain a unit-vector expression for a vector B one-fourth the length of A pointing in the same direction as A (c) Obtain a unit-vector expression for a vector C three times the length of A pointing in the direction opposite the direction of A

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 43P

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