ch03-p067

ch03-p067 - 67 The three vectors given are a = 5.0 b = 2.0...

This preview shows pages 1–2. Sign up to view the full content.

67. The three vectors given are ˆˆ ˆ 5.0 i 4.0 j 6.0 k ˆ 2.0 i 2.0 j 3.0 k ˆ 4.0 i 3.0 j 2.0 k a b c =+ =− + + + G G G (a) The vector equation rabc =−+ G GG G is ˆ [5.0 ( 2.0) 4.0]i (4.0 2.0 3.0)j ( 6.0 3.0 2.0)k ˆ =11i+5.0j 7.0k. r −+ +− + + + G (b) We find the angle from + z by “dotting” (taking the scalar product) G r with # k. Noting that 22 2 = | | = (11.0) + (5.0) + ( 7.0) = 14, rr G Eq. 3-20 with Eq. 3-23 leads to () ( ) k 7.0 14 1 cos 120 . r φφ ⋅= − = ¡ G G (c) To find the component of a vector in a certain direction, it is efficient to “dot” it (take the scalar product of it) with a unit-vector in that direction. In this case, we make the desired unit-vector by 2 ˆ 2.0i+2.0j+3.0k ˆ . || 2.0 (2.0) (3.0) b b b == + G G We therefore obtain ( ) ( ) 2 5.0 2.0 4.0 2.0 6.0 3.0 ˆ 4.9 . 2.0 (2.0) (3.0) b aa b + =⋅= = + G (d) One approach (if all we require is the magnitude) is to use the vector cross product, as the problem suggests; another (which supplies more information) is to subtract the result

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

Page1 / 2

ch03-p067 - 67 The three vectors given are a = 5.0 b = 2.0...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online