Chapter 9: Q. 56 (page 603)

If $P = (- 3, 1) a n d Q = (x, 4)$ , find all numbers x such that the vector represented by $\overset{⇀}{P Q}$ has length 5.

Short Answer

Expert verified

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

Step by step solution

Step. 1 Given

We have coordinates of two points,

$P \equiv (- 3, 1) a n d Q \equiv (x, 4)$

and, length of the vector

$\overset{⇀}{P Q} i s 5$

i.e.,

$|\overset{⇀}{P Q}| = 5$

Step. 2 Formula to find length of a vector

As we all know,

The length of the vector having coordinates $(x_{1}, y_{1}) a n d (x_{2}, y_{2})$ is

$\sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} u n i t s$

Now, $\overset{⇀}{P Q} = (x - (- 3)) \overset{⇀}{i} + (4 - 1) \overset{⇀}{j} \overset{⇀}{P Q} = (x + 3) \overset{⇀}{i} + 3 \overset{⇀}{j}$ ,

Step. 3 Calculating the value of x

Now we have,

$|\overset{⇀}{P Q}| = 5 \sqrt{{(x + 3)}^{2} + {(3)}^{2}} = 5$ ,

Squaring both sides we have,

${(x + 3)}^{2} + 9 = 25, {(x + 3)}^{2} = 16,$

Now taking square root both sides we get,

$(x + 3) = \pm 4, S o, x = \pm 4 - 3, i . e ., x = 1 o r - 7$

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If $P = (- 3, 1) a n d Q = (x, 4)$ , find all numbers x such that the vector represented by $\overset{⇀}{P Q}$ has length 5.

Short Answer

Step by step solution

Step. 1 Given

Step. 2 Formula to find length of a vector

Step. 3 Calculating the value of x

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

Short Answer

Step by step solution

Step. 1 Given

Step. 2 Formula to find length of a vector

Step. 3 Calculating the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

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Calculus

Study anywhere. Anytime. Across all devices.

If $P = (- 3, 1) a n d Q = (x, 4)$ , find all numbers x such that the vector represented by $\overset{⇀}{P Q}$ has length 5.