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Chapter 9: Q. 38 (page 630)

Find the distance from $P_{1} = (1, 3, - 2) t o P_{2} = (4, - 2, 1) .$

Short Answer

Expert verified

The distance from $P_{1} t o P_{2}$ is $\sqrt{43} .$

Step by step solution

01

Step 1. Given Information

The given two points are $P_{1} = (1, 3, - 2)$ and $P_{2} = (4, - 2, 1) .$

02

Step 2. Finding the distance

To find the distance from $P_{1} t o P_{2}$ , use the distance formula which is $d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}}$

So,

$d = \sqrt{{(4 - 1)}^{2} + {(- 2 - 3)}^{2} + {(1 - (- 2))}^{2}} d = \sqrt{9 + 25 + 9} d = \sqrt{43}$

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Most popular questions from this chapter

In Problems 13–28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$r \cos θ = 4$

Use the vectors in the figure at the right to graph each of the following vectors.

$2 u - 3 v + w$

Write the expression in the standard form $a + i b$ .

${[3 (\cos 80 ° + i \sin 80 °)]}^{3}$

Write the expression in the standard form $a + i b$ .

${[3 (\cos 80 ° + i \sin 80 °)]}^{3}$

In Problems 13–28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$r \sin θ = 4$

See all solutions

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