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Chapter 10: Q 26 (page 789)

Find the distance between the points (4, 5, 8,-2) and (-1, 3,-3, 6)

Short Answer

Expert verified

The required distance is $\sqrt{214}$

Step by step solution

01

Given information

The given points are (4, 5, 8,-2) and (-1, 3,-3, 6).

02

Finding the distance

The distance between the points as per formula is:

$\sqrt{{(- 1 - 4)}^{2} + {(3 - 5)}^{2} + {(- 3 - 8)}^{2} + {(6 - (- 2))}^{2}}$

Simplifying:

$\sqrt{25 + 4 + 121 + 64}$

Simplify further:

$\sqrt{214}$

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Most popular questions from this chapter

Suppose that we know the reciprocal rule for limits: If $\lim_{x \to c} g (x) = M$ exists and is nonzero, then $\lim_{x \to c} \frac{1}{g (x)} = \frac{1}{M}$ This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

If u and v are nonzero vectors in $ℝ^{3}$ , what is the geometric relationship between $u, v$ and $u \times v$ ?

Give an example of three vectors in $ℝ^{3}$ that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

Find a vector in the direction opposite to $<- 1, - 4, - 6>$ andwith magnitude 7.

Find the norm of the vector. $v = (3, - 4)$

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