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Chapter 9: Q. 56 (page 603)

If P=-3,1andQ=x,4, find all numbers x such that the vector represented by PQ鈬赌has length 5.

Short Answer

Expert verified

There will be two values for x which are -7 and 1.

Step by step solution

01

Step. 1 Given

We have coordinates of two points,

P鈮�-3,1andQ鈮�x,4

and, length of the vector

PQ鈬赌is5

i.e.,

PQ鈬赌=5

02

Step. 2 Formula to find length of a vector

As we all know,

The length of the vector having coordinates x1,y1andx2,y2is

x1-x22+y1-y22units

Now, PQ鈬赌=x--3i鈬赌+4-1j鈬赌PQ鈬赌=x+3i鈬赌+3j鈬赌,

03

Step. 3 Calculating the value of x

Now we have,

PQ鈬赌=5x+32+32=5,

Squaring both sides we have,

x+32+9=25,x+32=16,

Now taking square root both sides we get,

x+3=卤4,So,x=卤4-3,i.e.,x=1or-7

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