Vector in 3d with given by magnitude and angle

In summary, a vector in 3d with given magnitude and angle is a mathematical object that represents both the magnitude and direction of a physical quantity. It is typically represented by three components and can be calculated using trigonometric functions. A vector cannot have a negative magnitude, but its components can have negative values. Vectors can be represented graphically by drawing an arrow and have both magnitude and direction, while scalars only have magnitude.
  • #1
cbarker1
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Dear everyone,Direction Write the vector in component form.

v lies in the yz planeplane, has magnitude 2, and makes an angle of 30 degrees with the positive y axis.

Work
I know that the x component is zero.
<0,v1,v2​>

Thanks
Cbarker1
 
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  • #2

FAQ: Vector in 3d with given by magnitude and angle

What is a vector in 3d with given magnitude and angle?

A vector in 3d with given magnitude and angle is a mathematical object that represents both the magnitude and direction of a physical quantity. In three-dimensional space, a vector is typically represented by three components (x, y, z) and can be described by its magnitude (length) and angle with respect to a reference axis.

How do you calculate the components of a vector in 3d with given magnitude and angle?

To calculate the components of a vector in 3d with given magnitude and angle, you can use the trigonometric functions: cosine and sine. The x-component can be found by multiplying the magnitude by the cosine of the angle, while the y-component can be found by multiplying the magnitude by the sine of the angle. The z-component can be found by using the Pythagorean theorem, given the x and y components.

Can a vector in 3d have a negative magnitude?

No, a vector in 3d cannot have a negative magnitude. Magnitude is a measure of the length of a vector, and by definition, it cannot be negative. However, the components of a vector can have negative values, depending on their direction in relation to the reference axis.

How do you represent a vector in 3d with given magnitude and angle graphically?

A vector in 3d with given magnitude and angle can be represented graphically by drawing an arrow from the origin point to the endpoint. The length of the arrow represents the magnitude, and the angle with respect to the reference axis determines its direction. Additionally, the components of the vector can be represented by the x, y, and z axes.

What is the difference between a scalar and a vector in 3d with given magnitude and angle?

A scalar is a quantity that has only magnitude, such as time or temperature, while a vector has both magnitude and direction. In 3d, a scalar can be represented by a single number, while a vector requires three components to be fully described. Additionally, scalars can be added or subtracted by simply combining their values, while vector addition requires careful consideration of both magnitude and direction.

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