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Chapter 10: Q.22 (page 848)

Compute the volume of the parallelepiped determined by \(u=i\), \(v=2j\), and \(w=2k\).

Short Answer

Expert verified

The volume of the parallelepiped is \(4\) cu units.

Step by step solution

01

Given Information

The three vectors are \(u=i\), \(v=2j\), and \(w=2k\).

A parallelepiped form by these vectors. The volume of parallelepiped is given by,

\(V=|(u\times v)\cdot w|\).

02

Find the volume of parallelepiped

Substitute \(u\times v=2k\) and \(w=2k\) into formula.

\(\text{Volume }=|2k\cdot 2k|\)

\(\text{Volume }=4\)

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Most popular questions from this chapter

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=2,0,-5,v=-3,7,-1

What is the definition of the triple scalar product for vectors u, v and w in 鈩�3?

Suppose that we know the reciprocal rule for limits: If limx鈫�cg(x)=Mexists and is nonzero, then limx鈫�c1g(x)=1MThis 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.

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

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(Hint: Think of the xy-plane as part of 鈩�3.)

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