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Chapter 10: Q.18 (page 848)

Compute the area of the parallelogram determined by \(u\) and \(v\) where \(u=i\) and \(v=2j\).

Short Answer

Expert verified

The area of a parallelogram is \(2\) sq units.

Step by step solution

01

Given Information

The two vectors are \(u=i\) and \(v=2j\).

Area of parallelogram \(=|u\times v|\).

02

Find the area of a parallelogram

\(\text{Area }=\begin{vmatrix}i&j&k\\1&0&0\\0&2&0\end{vmatrix}\)

\(\text{Area }=|0i+0j+2k|\)

\(\text{Area }=2\)

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Most popular questions from this chapter

In Exercises 30–35 compute the indicated quantities when u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

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Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is k=1.

(b) True or False: ∑k=0n 1k+1+∑k=1n k2is equal to ∑k=0n k3+k2+1k+1.

(c) True or False: ∑k=1n 1k+1+∑k=0n k2is equal to ∑k=1n k3+k2+1k+1 .

(d) True or False: ∑k=1n 1k+1∑k=1n k2 is equal to ∑k=1n k2k+1.

(e) True or False: ∑k=0m k+∑k=mn kis equal to∑k=0n k.

(f) True or False: ∑k=0n ak=−a0−an+∑k=1n−1 ak.

(g) True or False: ∑k=110 ak2=∑k=110 ak2.

(h) True or False: ∑k=1n ex2=exex+12ex+16.

What is meant by the triangle determined by vectors u and v in ℝ3? How do you find the area of this triangle?
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