Calculating Vector Projection Using Trigonometry

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In summary, a vector problem is a mathematical problem that involves using vectors to find a solution. Some real-world examples include calculating forces, velocities, and displacements. To solve a vector problem, you need to find the magnitude and direction of each vector and use vector addition or subtraction to find the resultant vector. The main difference between a scalar and a vector is that a scalar only has magnitude, while a vector has both magnitude and direction. Common strategies for solving vector problems include drawing diagrams, breaking down vectors, using trigonometry, and applying the Pythagorean theorem.
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Two vectors are given by avector = 3.5i + 4.5j and bvector = 2.0i + 5.0j. Find the following:

(a) avector x bvector

(b) avector ·bvector

(c) (avector + bvector ) · bvector

(d) the component of avector along the direction of bvector
these are the answers i got

a)8.5k
b) 29.5
c) 58.5
d)16.2

i know that a through c are correct but d is incorrect, i calculated d by

cos-1 (29.5/(5.7*5.39) = 16.2

the 5.7 came from sqrt(3.5²+4.5²)
5.39 came from sqrt(2²+5²)

thanks in advance
 
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OK, so the angle between the vectors is 16 degrees. What did you do to calculate the projection of A on B?
 

What is a vector problem?

A vector problem is a mathematical problem that involves using vectors, which are quantities that have both magnitude and direction, to find a solution.

What are some real-world examples of vector problems?

Some examples of vector problems in real-life include calculating the direction and magnitude of a force on an object, finding the velocity and acceleration of an object moving in a certain direction, and determining the displacement of an object.

How do you solve a vector problem?

To solve a vector problem, you need to find the magnitude and direction of each vector involved and then use vector addition or subtraction to find the resultant vector. This resultant vector represents the final solution to the problem.

What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, speed, and time, while examples of vectors include displacement, force, and velocity.

What are some common strategies for solving vector problems?

Some common strategies for solving vector problems include drawing a diagram to visualize the vectors, breaking down a vector into its x- and y-components, using trigonometry to find the magnitude and direction of a vector, and using the Pythagorean theorem to find the resultant vector.

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