Parallel and perpendicular vectors with given magnitude

In summary, to find the dot product of two vectors A and B, we use the formula AB = AxBx + AyBy + AzBz. The dot product of A and B is 186. The cross product of A and B is 118i + 18j -96k. The angle between the vectors is 42 degrees. To find a vector C that is parallel with A and has the same magnitude as B, we can simply use a scaled version of vector A. To find a vector C that is perpendicular to A and has the same magnitude as B, we can find a unit vector in the same direction as A and then multiply it by the magnitude of B. We can find a unit vector in the
  • #1
demv18
3
0

Homework Statement


Given two vectors A=9i+1j+9k and B=12i-12j+10k find:
a) Their dot product AB
b) Their cross product AxB
c)The angle between the vectors A and B
d) a vector C that is parallel with A and has the same magnitude as B
e) A vector C that is perpendicular to A and has the same magnitude as B


Homework Equations


dot product: AB=AxBx+AyBy+AzBz


The Attempt at a Solution


I got a, b, and c.
a) (9)(12)+(1)(-12)+(9)(10)=186
b) 118i+18j-96k
c) 42 deg.
d and e) I have no idea how to get the vector to be parallel or perpendicular to A with the same magnitude as B. Just want a simple explanation please!
 
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  • #2
demv18 said:

Homework Statement


Given two vectors A=9i+1j+9k and B=12i-12j+10k find:
a) Their dot product AB
b) Their cross product AxB
c)The angle between the vectors A and B
d) a vector C that is parallel with A and has the same magnitude as B
e) A vector C that is perpendicular to A and has the same magnitude as B


Homework Equations


dot product: AB=AxBx+AyBy+AzBz


The Attempt at a Solution


I got a, b, and c.
a) (9)(12)+(1)(-12)+(9)(10)=186
b) 118i+18j-96k
c) 42 deg.
d and e) I have no idea how to get the vector to be parallel or perpendicular to A with the same magnitude as B. Just want a simple explanation please!

A parallel vector will simply lie along the same vector. So a scaled version of the vector will do.

For a perpendicular vector, what is the property of the cross product concerning the direction of the resulting vector?

Sometimes it's handy to find unit vectors in the desired directions and then multiply the unit vector by the desired magnitude. Do you know how to find a unit vector in the same direction as a given vector?
 

Related to Parallel and perpendicular vectors with given magnitude

What are parallel and perpendicular vectors with given magnitude?

Parallel vectors are vectors that have the same direction, but can have different magnitudes. Perpendicular vectors are vectors that have a 90 degree angle between them, meaning they intersect at a right angle. With given magnitudes, these vectors can be expressed using mathematical equations.

How are parallel and perpendicular vectors with given magnitude calculated?

To calculate parallel vectors with given magnitude, you can use the formula: v = c * u, where v is the parallel vector, c is a scalar (a number), and u is the original vector. To calculate perpendicular vectors with given magnitude, you can use the formula: v = c * v, where v is the perpendicular vector, c is a scalar, and v is the original vector.

What are some real-world applications of parallel and perpendicular vectors with given magnitude?

Parallel and perpendicular vectors with given magnitude are used in various fields, such as engineering, physics, and computer graphics. They are used to represent forces, motion, and geometric transformations. For example, in engineering, they are used to calculate the direction and magnitude of forces acting on a structure. In computer graphics, they are used to create realistic 3D models by representing the direction and intensity of light sources.

What is the significance of the magnitude in parallel and perpendicular vectors?

The magnitude in parallel and perpendicular vectors is important because it determines the length of the vector. In parallel vectors, the magnitude can be any positive number, as long as it is multiplied by the original vector's direction. In perpendicular vectors, the magnitude must be equal to the length of the original vector, as it is multiplied by the original vector's direction to create a perpendicular vector.

Can two vectors with the same magnitude be both parallel and perpendicular?

No, two vectors with the same magnitude cannot be both parallel and perpendicular. This is because parallel vectors must have the same direction, while perpendicular vectors must have a 90 degree angle between them. If two vectors have the same magnitude, they can either be parallel or perpendicular, but not both.

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