Chap03-Solution - Chap.3 HW Questions v v 3. Equation 3-2...

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1 Chap.3 HW Questions 3. Equation 3-2 shows that the addition of two vectors b a v v and is commutative. Does that mean subtraction is commutative, so that a b b a v v v v = ? ( ) ( ) a b b a b a v v v v v v = + = - . Answer: NO 7. Which of the arrangements of axes can be labeled “right- handed coordinate system”? As usual, each axis label indicates the positive side of the axis. a ,b ,c, d, f are right handed. e is not right-handed 9. If B v q F v v v × = and v v is perpendicular to B v , then what is the direction of B v in the three situations shown in Figure 3-25 when constant q is (a) positive and (b) negative? Using the RHR (right hand rule) (a): (1) +x, (2) +z, (3) +z; (b) (1) -x, (2) –z (3) –z.
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2 Problems 15. Two vectors are given by () k ˆ m 4.0 j ˆ m 1.0 i ˆ m) 0 . 1 ( k ˆ m 1.0 j ˆ m 3.0 i ˆ m) 0 . 4 ( + + = + = b a v v In unit-vector notation, find (a) b a v v + , (b) b a v v , and (c) a third vector c v such that 0 = + c b a v v v . (a) ˆˆ ˆ ˆ ˆ ˆ [4.0 ( 1.0)] i [( 3.0) 1.0] j (1.0 4.0)k 3.0i 2.0j 5.0 k. ab += +− +− + + + = + r r (b) ˆ ˆ ˆ ˆ [4.0 ( 1.0)]i [( 3.0) 1.0]j (1.0 4.0)k 5.0 i 4.0 j 3.0 k. −= −− +− − + = r r (c) The requirement r r r abc −+ = 0 leads to ( ) b a c v v r = . Using the result of part b) ˆ 5.0i + 4.0 j + 3.0k. c =− r 22. Oasis B is 25 km due east of oasis A . Starting from oasis A , a camel walks 24 km in a direction 15° south of east and then walks 8.0 km due north. How far is the camel then from oasis B ?
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Chap03-Solution - Chap.3 HW Questions v v 3. Equation 3-2...

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