VAM_49-59

# VAM_49-59 - Tutorial V AM V ector Algebra and an...

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

Tutorial VAM: Vector Algebra andan Introduction to Matrices n 2 ¢ r =17 x +19 y +20 z = n 2 ¢ A =75 : The equations describing the line can thus be expresses parametrically as x = t; y =5 ¡ 3 t; z = ¡ 1 +2 t: The distance from the origin to the line is d = j ^ n 2 ¢ A j = 75 = p 17 2 +19 2 +20 2 = 5 p 42 = 14 : Exercise 49. Let the angle between A and ^x 1 be μ: Then, remembering that A 0 = A; a 0 1 = A 0 cos( μ + ' ) = A (cos μ cos ' ¡ sin μ sin ' ) = a 1 cos ' ¡ a 2 sin ': a 0 2 = A 0 sin( μ + ' ) = A (cos μ sin ' +sin μ cos ' ) = a 1 sin ' + a 2 cos ': These equations can be written in matrix form as in Eqn. 77. Exercise 50. R (2) (30 ± ) = μ cos(30 ± ) ¡ sin(30 ± ) sin(30 ± ) cos(30 ± ) = 1 2 μ p 3 ¡ 1 1 p 3 : Exercise 51. Let B also be rotated by R (2) ( ' ) : μ b 0 1 b 0 2 = μ cos ' ¡ sin ' sin ' cos ' ¶μ b 1 b 2 : Then, A 0 ¢ B 0 = a 0 1 b 0 1 + a 0 2 b 0 2 = ( a 1 cos ' ¡ a 2 sin ' )( b 1 cos ' ¡ b 2 sin ' ) +( a 1 sin ' + a 2 cos ' ) ( b 1 sin ' + b 2 cos ' ) = a

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 / 3

VAM_49-59 - Tutorial V AM V ector Algebra and an...

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

View Full Document
Ask a homework question - tutors are online