What’s Your Vector, Victor

Section 10.4, 10.5

In a Nutshell

By Fr Chris

<5,5>

<4,-1>

<5+4,4-1>=<9,3>

New School: v + z=w

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5v i + 5

v j ( ) + 4

v i −

v j ( ) = 9

v i + 4

v j

Magnitude of w=9i+4j:

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9v i + 4

v j = 92 + 42 = 97

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θ

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cosθ =v v ⋅

v w

v v

v w

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=(5 ⋅9) + (5 ⋅4)

(5 5)( 97)= .5903

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θ =cos−1(.5903) ≈ 53.8°v=5i+5j

w=9i+4j

z=4i-1j

When are vectors orthogonal (perpendicular)?

When the angle is 90° , and the cos(90°)=0, right?

v and w are orthogonal when v•w=0

v= 3i+4j, w= 8i-6j. Orthogonal??

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vv ⋅

v w = (3)(8) + (4)(−6) = 24 − 24 = 0

YES!

10.5 # 21. Current goes 3 kph East. Boat goes 20 kph. What angle should you steer to go North?

θ

θ

3i

20j3i+20j

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cosθ =20

v j ⋅ 3

v i + 20

v j ( ) ⋅

20v j 3

v i + 20

v j

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=(0)(3) + (20)(20)

(20)( 409)

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=400

404.474968≈ .9889

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θ =cos−1 .9889 ≈ 8.6°

The magnitude of 3i+20j=

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409Time=Distance/Rate

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x =12 /cos8.6

409≈1.5min