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.
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.
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.
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.
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.