7.6_bzat4e - Example The wind is blowing at 16 mph in the...

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Section 7.6 Vectors
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Directed Line Segments and Geometric Vectors
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Example -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y u v (2,3) ( 2, 1) - - ( 4, 4) - - Show that u=v.
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Vectors in the Rectangular Coordinate System
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Example -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y Sketch the vector v=-2i+j and find its magnitude.
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Example -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 1 2 Let v be a vector from initial point P ( 2, 2) to terminal pont P (2,3). Write v in terms of i and j. - -
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Operations with Vectors in Terms of i and j
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Example If v=2i-3j and w=-i+4j find each of the following: a. v+w b. v-w c. 2v d. -3w e. 2v-3w
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Unit Vectors
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Example Find the unit vector in the same direction as v=-3i-4j. Then verify that the vector has the magnitude of 1.
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Writing a Vector in Terms of Its Magnitude and Direction
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Unformatted text preview: Example The wind is blowing at 16 mph in the direction of N60 E. Express its velocity as a vector v in terms of i and j. Application Example 1 2 1 2 Two forces F and F , of magnitude 5 lbs and 12 lbs, respectively act on an object. The direction of F is N20 E and the direction of F is N75 E. Find the magnitude and the direction of the resultant force. Express the magnitude to the nearest hundredth of a pound and the direction angle to the nearest tenth of a degree. (a) (b) (c) (d) If u=- 3i+4j, v=2i-j find 2u+v-i+3j 4i-j 5i+3j-4i+7j (a) (b) (c) (d) Find the magnitude of the vector v=-3i+4j 5 6 7 8...
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7.6_bzat4e - Example The wind is blowing at 16 mph in the...

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