Lecture03_Vectors_Review

# Lecture03_Vectors_Review - P7.3-47 Given | F |= 30 N r d =<...

This preview shows pages 1–4. Sign up to view the full content.

18 Work done by w (gravity force) = w . d = 0 ( w d ) Work done by F (applied force) = F . d = |F|.|d| cos θ ( d // F ) = 150 N.m m d N F > =< = 3 , 4 30 || || r P7.3-47 : Given weight

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

View Full Document
19 Properties of Dot Product ± a . b = 0 if a = 0 or b = 0 ± a . b = b . a (commutative law) ± a . ( b + c )= a . b + a . c (distributive law) ± a . ( k b )= ±( k a ) . b = k ( a.b ) k a scalar ± a . a 0 ± a . a = || a || 2 ± For nonzero vectors a and b (i) a . b > 0 if and only if θ is acute (ii) a . b < 0 if and only if θ is obtuse, and (iii) a . b = 0 if and only of if cos θ =0 ( Orthogonal vectors ) Theorem 7.1 Criterion for Orthogonal Vectors Two nonzero vectors a and b are orthogonal if and only if a . b
Angle Between Two Vectors: || || || || || || || || cos 3 3 2 2 1 1 b a b a b a b a b a b a + + = = r r θ 27 2 14 cos = o 9 . 44 77 . 0 9 42 cos 1 = ± Example Find the angle between a = 2 i +3 j + k & b = - i +5 j + k =14, Solution:

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.

{[ snackBarMessage ]}

### Page1 / 9

Lecture03_Vectors_Review - P7.3-47 Given | F |= 30 N r d =<...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online