Finding the Direction of a Vector: Solving a Problem with Vectors

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In summary, a vector is a mathematical quantity with both magnitude and direction, represented as an arrow. The direction of a vector can be found using trigonometric functions or the inverse tangent function. Vectors can be added or subtracted using specific rules. To solve problems with vectors, one can use vector operations, components, and trigonometric functions. Vectors have many real-world applications in physics, engineering, and navigation. They can represent physical quantities and describe movement and displacement.
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teffy3001
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ive been trying to do this problem but i don't know where to start...any help?


let v be a vector of length 9 in the direction 65degrees south of west.

if u has the same direction as v, and if 3|u| = 2|v|, then which of the following can be used to describe u?


u = 5.705i + 12.235j
u = -2.536i - 5.438j
u = 2.536i + 5.438j
u = -5.705i - 12.235j
none of these
 
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What is the magnitude of u? From that find the components of u.
 

FAQ: Finding the Direction of a Vector: Solving a Problem with Vectors

What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is represented as an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

How do you find the direction of a vector?

To find the direction of a vector, you can use the trigonometric functions sine, cosine, and tangent. These functions can be used to calculate the angle between the vector and a reference axis. Alternatively, you can also use the inverse tangent function to calculate the angle directly from the components of the vector.

Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using vector addition and subtraction rules. For example, to add two vectors, you can place the tail of one vector at the head of the other vector and then draw a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the sum of the two original vectors.

How do you solve a problem with vectors?

To solve a problem with vectors, you can use the properties and rules of vector operations, such as addition, subtraction, and scalar multiplication. You can also use vector components and trigonometric functions to break down the vector into smaller parts and then solve for the desired quantity.

Can vectors be used in real-world applications?

Yes, vectors have many real-world applications, such as in physics, engineering, and navigation. They can be used to represent physical quantities such as force, velocity, and acceleration, and can also be used to describe the direction and magnitude of movement and displacement in various systems.

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