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Chapter 10: Q. 61 (page 802)

Let cand dbe a scalars and let v be a vector in R3. Show that the following distributive property holds: role="math" localid="1663644928733" (c+d)v=cv+dv

Short Answer

Expert verified

It is proved that,(c+d)v=cv+dv

Step by step solution

01

Consider a vector

Let us assume a vector in R3

v=i+j+k

The scalersc=1andd=2

02

Proof

Let us consider the LHS of the given expression,

LHS=(c+d)v=(1+2)(i+j+k)=3(i+j+k)=3i+3j+3kRHS=cv+dv=1(i+j+k)+2(i+j+k)=i+j+k+2i+2j+2k=3i+3j+3k

Since, LHS=RHS

Hence, proved.

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Most popular questions from this chapter

Give an example of three nonzero vectors u, v and w in 鈩�3 such that u脳v=u脳w but v鈮�w. What geometric relationship must the three vectors have for this to happen?

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=22,12,12

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.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(4,鈭�2),Q(鈭�2,0),R(1,鈭�5)

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

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

v脳wandw脳v

Find vand find the unit vector in the direction of v.

v=3,鈭�4
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