1 / 9

a) Which pair(s) of vectors form opposite vectors? _______________________

MTH-5110 Pretest. 1. Five vectors are represented on the following Cartesian plane. a) Which pair(s) of vectors form opposite vectors? _______________________ b) Which pair(s) of vectors form orthogonal vectors? ______________________

burt
Download Presentation

a) Which pair(s) of vectors form opposite vectors? _______________________

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. MTH-5110 Pretest 1. Five vectors are represented on the following Cartesian plane. a) Which pair(s) of vectors form opposite vectors? _______________________ b) Which pair(s) of vectors form orthogonal vectors? ______________________ c) Name the vector(s) that could form a vector basis with vector w. ___________ 2. From the three expressions given below, determine which one is true. State the property associated with the true expression.

  2. SCALE • A small plane flies in a direction N 35° W at 250 km/h. A wind blows to the south at 55 km/h to change its direction. Construct a vector diagram to show the resultant. • Given the following ordered pairs: A (-1, 3), B (3.5, 4), C (5, -2) and D (1, -5), use the algebraic method to calculate the components of the resultant vector, r.

  3. N swimmer 30° current • Two forces, one 150 N and the other 220 N are applied to the same object. The first force is oriented SW and the second at 125°. What single force would have the same effect on this object? • A swimmer crosses a river in a direction S 30° W at a speed of 2.5 km/h. A current of 1 km/h towards the east changes the swimmer’s direction. What is the angle of deviation from the intended direction.

  4. Calculate the components of the resultant vector w. • Determine coefficients k1 and k2 of this linear combination.

  5. 190 N 43° 150 m • Given vectors u and v below: • Solve the following problems. • A mother pulls her child in a sleigh. The rope on the sleigh makes a 43° angle with the horizontal and she pulls with a force of 190 N to cause it to move. How much work (in kilojoules) is done to make the sleigh move 150 m.

  6. B Scalar product of orthogonal vectors Definition of an altitude A C P Definition of a norm of a vector • Using vector theory, complete the following proof. • In a right triangle, the measure of a side adjacent to the right angle is the geometric mean of its projection and the hypotenuse. Approach: We can apply the definition of a norm of a vector to side AB and rewrite side AB as the sum of vectors using Chasles relation. The expression can be transformed to eventually reach the sired conclusion.

  7. y B (4,7) A (-5,5) C (11,1) D (2,-1) x • Prove that quadrilateral ABCD represented below is a rhombus. • Using the vectors below, prove that the addition of vectors is associative.

  8. B A C D • Triangle ABC is a right triangle whose altitude is segment AD. Determine whether the statements concerning this figure are true or false. Adjust the false statements to make them true. • A ferry is used to transport passenger vehicles between Cap-Rouge and Cap-Espoir, a distance of 8 km. Its direction with respect to Cap-Rouge is N 35º E. The current of the river that the ferry crosses is 3.5 km/h to the west. So as to land at the Cap-Espoir in one hour, at what speed and in what direction should the captain set out in the ferry? CAP-ESPOIR N Direction of current 8 km 35º W E CAP-ROUGE S

  9. Given the following ordered pairs: A (-5.2, -3), B (-3, 2.5), C (-1, 7) and D (3.3, -4), Using the scalar product, calculate the angle between vectors s and t.

More Related