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Chapter 11: Q. 17 (page 860)

What is the dot product of the vector functions r1(t)=x1(t),y1(t)andr2(t)=x2(t),y2(t)?

Short Answer

Expert verified

The dot product of the given two vector functions isx1(t)x2(t)+y1(t)y2(t).

Step by step solution

01

Step 1. Given Information.

The given vector functions arer1(t)=x1(t),y1(t)andr2(t)=x2(t),y2(t).

02

Step 2. Find the dot product.

Let's find the dot product,

r1t路r2t=x1(t),y1(t)路x2(t),y2(t)=x1(t)i+y1(t)j路x2(t)i+y2(t)j=x1(t)x2(t)i路i+x1(t)y2(t)i路j+y1(t)x2(t)j路i+y1(t)y2(t)j路jSincei路i=1,i路j=0,j路i=0,j路j=1=x1(t)x2(t)+y1(t)y2(t)

Thus, the product of two vector functions is a scalar function.

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