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Chapter 9: Q. 55 (page 603)

If v鈬赌=2i鈬赌-j鈬赌and w鈬赌=xi鈬赌+3j鈬赌, find all numbers x for which v鈬赌+w鈬赌=5.

Short Answer

Expert verified

There will be two such values of x which are21-2and-21-2

Step by step solution

01

Step. 1 Given

v鈬赌=2i鈬赌-j鈬赌andw鈬赌=xi鈬赌+3j鈬赌

02

Step. 2 Magnitude of a vector

Firstly, we need to find the vector v鈬赌+w鈬赌,

so,

v鈬赌+w鈬赌=(2i鈬赌-j鈬赌)+(xi鈬赌+3j鈬赌)v鈬赌+w鈬赌=(2i鈬赌+xi鈬赌)+(-j鈬赌+3j鈬赌)v鈬赌+w鈬赌=(x+2)i鈬赌+2j鈬赌

we get the vector whose magnitude is given i.e., 5

So,v鈬赌+w鈬赌=5(x+2)2+(2)2=5

03

Step. 3 Final solution

Now we have one equation in one variable. Solve it for x,

(x+2)2+4=5,

Squaring both sides we get,

(x+2)2+4=25(x+2)2=21,

Taking square root both sides we get,

(x+2)=卤21,x=卤21-2,

So,

x=21-2orx=-21-2

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