# UCSD MATH 10C - Lecture Examples (2 pages)

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## Lecture Examples

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## Lecture Examples

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Pages:
2
School:
University of California, San Diego
Course:
Math 10c - Calculus III
##### Calculus III Documents

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10 14 08 Math 10C Lecture Examples Section 12 3 The dot product Calculate v w for v h6 2i and w h4 3i Example 1 Answer v w 18 What is v w for v h6 2 3i and w h4 3 6i Example 2 Answer v w 0 Find an angle between the vectors v h4 1i and w h2 4i in Figure 1 Give exact and approximate decimal values Example 3 y w h2 4i 4 2 FIGURE 1 Answer Example 4 v h4 1i 2 cos 1 12 17 20 4 x 0 862 radians Find the constant k such that the vectors h 3 1i and hk 2i are perpendicular Then draw the two vectors 2 The vectors are h 23 2i and h 3 1i Figure A4 Answer k 3 y 2 2 3 2 h 3 1i 2 Figure A4 Lecture h 32 2i notes to accompany Section 12 3 of Calculus by Hughes Hallett et al 1 x Math 10C Lecture Examples 10 14 08 Example 5 Section 12 3 p 2 Give an equation of the plane through the point 2 3 4 and perpendicular to the vector h 6 5 4i 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 3x 5y 6z 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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