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The following questions refer to the vectors depicted by arrows in figure 1.57.

(a) What are the components of the vector a?(note that since the vector lies in the xy plane ,its z component is zero.)

(b) What are the components of the vector b?

(c) Is this statement true or false?a=b

(d) What are the components of the vector c?

(e) Is this statement true or false?c=-a

(f) What are the components of the vector d?

(g) Is this statement true or false? d=-c

Short Answer

Expert verified

(a) The component of the vector a=-4,-3,0.

(b) The component of the vectorb=-4,-3,0.

(c) Statement a=bis true .

(d) The component of the vector c=4,3,0.

(e) Statement c=-a is true.

(f) The component of the vector d=-3,4,0.

(g) Statement d=-c is false.

Step by step solution

01

Vector components

The vector has three components. These three components are the unit cut by the vector on x, y and z axis. The vector components can be represented by the following manner.

Let the vector is r, then the vector component of the vector r will be,

r=rx,ry,rz

Where,rxisxaxisunit,ryisyaxisunit,rziszcomponentunit.

02

(a) Component of vector a→

All the vectors have zero z component here because the z dimension is absent. The component for the vector a covering the 4 unit of x axis and 3 unit of y axis in 3rd coordination centre of the graph hence the component of the vectora=-4,-3,0.

03

(b) Component of vector b→

All the vectors have zero z component here because the z dimension is absent. The component for the vector b covering the 4 unit of x axis and 3 unit of y axis in 3rd coordination centre of the graph hence the component of the vector b=-4,-3,0.

04

(c) Statement a→=b→

Vector a=-4,-3,0and the vector b=-4,-3,0. Both the vector components are equal hence statementa=b is true.

05

(d) Component of vector c→

All the vectors have zero z component here because the z dimension is absent. The component for the vector c covering the 4 unit of x axis and 3 unit of y axis in 4th coordination centre of the graph hence the component of the vector c=4,3,0.

06

(e) Statement c→=-a→

Vector a=-4,-3,0and the vector c=4,3,0. Both the vector components are just opposite to each other hence statement c=-a is true.

07

(f) Component of vector d→

All the vectors have zero z component here because the z dimension is absent. The component for the vector d covering the 3 unit of x axis in 4th and 4 unit of y axis in 1st coordination centre of the graph hence the component of the vector d=-3,4,0.

08

(g) Statement d→=-c→

Vector d=-3,4,0and the vector c=4,3,0. Both the vector components are not opposite to each other hence statementd=-c is false.

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