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HH_13_3 - a-6 5-4 A Answer-6 x-2 5 y-3-4 z-4 = 0 Example 6...

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(10/14/08) Math 10C. Lecture Examples. Section 12.3. The dot product Example 1 Calculate v · w for v = a 6 , - 2 A and w = a 4 , 3 A . Answer: v · w = 18. Example 2 What is v · w for v = a 6 , - 2 , 3 A and w = a 4 , 3 , - 6 A ? Answer: v · w = 0 Example 3 Find an angle θ between the vectors v = a 4 , 1 A and w = a 2 , 4 A in Figure 1. Give exact and approximate decimal values. x 2 4 y 2 4 v = a 4 , 1 A w = a 2 , 4 A θ FIGURE 1 Answer: θ = cos –1 p 12 17 20 P . = 0 . 862 radians Example 4 Find the constant k such that the vectors a- 3 , - 1 A and a k , - 2 A are perpendicular. Then draw the two vectors. Answer: k = 2 3 The vectors are a 2 3 , - 2 A and a- 3 , - 1 A . Figure A4 x 2 y 2 - 2 a- 3 , - 1 A a 2 3 , - 2 A 2 3 Figure A4 Lecture notes to accompany Section 12.3 of Calculus by Hughes-Hallett et al. 1
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Math 10C. Lecture Examples. (10/14/08) Section 12.3, p. 2 Example 5 Give an equation of the plane through the point ( 2 , 3 , 4 ) and perpendicular to the vector
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Unformatted text preview: a-6 , 5 ,-4 A . Answer:-6( x-2) + 5( y-3)-4( z-4) = 0 Example 6 Give an equation of the plane through the point ( 1 ,-1 , 2 ) that is parallel to the plane 3x-5y + 6z = 10 . Answer: 3( x-1)-5( y + 1) + 6( z-2) = 0 or (written) 3 x-5 y + 6 z = 20. Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 12.2: Examples 1 and 2 Section 12.5: Examples 5 and 6 ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course....
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HH_13_3 - a-6 5-4 A Answer-6 x-2 5 y-3-4 z-4 = 0 Example 6...

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