Solve Vector Problems: Displacements & Components | Find r, Angle, & Components

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In summary, vectors are mathematical quantities that have both magnitude and direction and can represent physical quantities such as displacement, velocity, and force. Common problems with vectors include finding the resultant vector, determining the direction and magnitude, and solving equations. To add or subtract vectors, they must be broken down into components and then added or subtracted separately. Vectors cannot be multiplied, but can be multiplied by a scalar to scale their magnitude. Vectors are used in various real-world applications such as physics, engineering, and computer graphics to represent and analyze physical quantities, model motion, and create visual effects.
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noname1
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Here are three displacements, each in meters:
d1 = 9i + 5j - 3k
d2 = -1i + 1j + 3k
d3 = 4i + 3j + 2k What is r = d1 - d2 + d3 ((a), (b) and (c) for i, j and k components respectively)?
(d) What is the angle between r and the positive z axis?
(e) What is the component of d1 along the direction of d2?
(f) What is the component of d1 that is perpendicular to the direction of d2 and in the plane of d1 and d2?a) 14i
b) 7j
c) -4k
d) cos-1(-4/sqrt14²+7²+4²) = 104.3
e) (-9+5-9)/(sqrt(1²+²+3²) = -3.92i am having difficulty with e and f i tried e not sure if right but don't understand f

thanks in advance
 
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f) [(magnitude of d1)^2 - (the component of d1 along the direction of d2)^2]^1/2
 

Related to Solve Vector Problems: Displacements & Components | Find r, Angle, & Components

1. What are vectors and what do they represent?

Vectors are mathematical quantities that have both magnitude and direction. They can represent physical quantities such as displacement, velocity, and force.

2. What are some common problems that arise when working with vectors?

Some common problems with vectors include finding the resultant vector, determining the direction and magnitude of a vector, and solving vector equations.

3. How do you add or subtract vectors?

To add or subtract vectors, you must first break them down into their respective components along the x and y axes. Then, add or subtract the components separately to find the resultant vector.

4. Can vectors be multiplied?

No, vectors cannot be multiplied. However, they can be multiplied by a scalar, which is a single number that scales the magnitude of the vector without changing its direction.

5. How are vectors used in real-world applications?

Vectors are used in various fields such as physics, engineering, and computer graphics. They are used to represent and analyze physical quantities, model and simulate motion, and create visual effects in animations and video games.

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