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Chapter 3: Q57P (page 60)

If B鈫�is added to A鈫�, the result is6.0i^+1.0j^ . If B鈫�is subtracted fromrole="math" localid="1656310989938" A鈫� , the result is -4.0i^+7.0j^. What is the magnitude of role="math" localid="1656311031101" A鈫�?

Short Answer

Expert verified

The magnitude ofA鈫� is 4.1

Step by step solution

01

To understand the concept

This problem deals with the addition and subtraction of vectors.

02

To find the magnitude of A→

Given,

A鈫�+B鈫�=6.0i^+1.0j^(i)A鈫�-B鈫�=-4.0i^+7.0j^(ii)

Adding equations (i) and (ii),

(A鈫�+B鈫�)+(A鈫�-B鈫�)=(6.0i^+1.0j^)+(-4.0i^+7.0j)2A鈫�鈨�=(2.0i^+8.0j^)

Thus

A鈫�=(1.0i^+4.0j^) (iii)

Using equation (iii), the magnitude of A鈫�is then given by

A=|A鈨�|=Ax2+Ay2A=(1.0)2+(4.0)2A=4.1

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Most popular questions from this chapter

A wheel with a radius of 45.0 cmrolls without slipping along a horizontal floor (Fig). At time t, the dot P painted on the rim of the wheel is at the point of contact between the wheel and the floor. At a later time t2, the wheel has rolled through one-half of a revolution. What are (a) the magnitude and (b) the angle (relative to the floor) of the displacement of P?

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Ifa鈫�-b鈫�=2c鈫�,a鈫�+b鈫�=4c鈫�andc=3.0i^+4.0j^then what are (a)a^and (b)b^?
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