Question

In: Physics

1) Two vectors, r and s lie in the x y plane. Their magnitudes are 4.84 and...

1) Two vectors, r and s lie in the x y plane. Their magnitudes are 4.84 and 6.09 units respectively, and their directions are 341^o and 65.0^o respectively, as measured counterclockwise from the positive x axis. What are the values of vectors (a) r . s and (b) | r × s |?

2) For the following three vectors A B C, what is 3⋅C . (3A × B) ?
A =3.00î + 2.00ĵ - 3.00k̂
B =-4.00î + 3.00ĵ + 3.00k̂
C =6.00î - 7.00ĵ

Expert Solution

given

|r| = 4.84

|s| = 6.09

_r = 341^o

_s = 65^o

_rs = ( 341 - 65 )

= 276^o

a )

r.s = |r| |s| cos_rs

= 4.84 x 6.09 x cos276

r.s = 3.081 units

b )

r x s = |r| |s| sin_rs

= 4.84 x 6.09 x sin276

r x s = - 29.314 units

2 )

given

A = 3.00 î + 2.00 ĵ - 3.00 k̂

B = - 4.00 î + 3.00 ĵ + 3.00 k̂

C = 6.00 î - 7.00 ĵ

3C . ( 3A x B )

3C = 3 x ( 6.00 î - 7.00 ĵ )

= 18 i - 21 j

3 A = 3 x ( 3.00 î + 2.00 ĵ - 3.00 k̂ )

= 9 i + 6 j - 9 k

| i j k |

( 3A x B ) = | 9 6 -9 |

| - 4 3 3 |

= i ( 18 + 27 ) - j ( 27 - 36 ) + k ( 27 + 24 )

( 3A x B ) = 45 i + 9 j + 51 k

3C . ( 3A x B ) = ( 18 i - 21 j ).(45 i + 9 j + 51 k)

= ( 18 x 45 ) + ( -21 x 9 ) + 0

3C . ( 3A x B ) = 621 units

genius_generous answered 2 hours ago

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