Geometric and Cartesian Vectors

Unit 1: Geometric Vectors

A ship heading of 143° at 18 Knots. 10 Knot current at bearing 112°. Ground Velocity?

x²=18²+10²-2(18)(10)cos149

=27.1 Knots

SinΘ = Sin149 Bearing

10 27.1 149-11= 132°

SinΘ=Sin149(10)

27.1

Θ=11°

Unit 2: Cartesian Vectors

Vectors a=[3,-7,8], b=[-6,3,4], c=[2,5,7] evaluate:

A) a + 2b B) B * C

=[3,-7,8]+2[-6,3,4] =[3,-7,8]+[-12,6,8] =[-9,-1,16] =31

C) a x c

=[-7(7)-5(8),8(2)-7(3),3(5)-2(-7)] [-89,-5,29] 5 7 2 5

Ex 2) A(2,3,5) B(5,10,-3) Determine:

A) ab B) |ab|

=[5-2,10-3,-3-5] =√3²+7²+8²

=[3,7,-8] =√122

Ex 3) Determine a x b

a x b= |a| |b| sinΘ n

=20(30)sin32 n

= 317.95 n

n is into the page