Wiki User
∙ 10y agoConsider any two points on the vector, P = (a, b) and Q = (c, d). And lext x be the angle made by the vector with the positive direction of the x-axis.
Then either a = c, so that the vector is vertical and its direction is straight up or a - c is non-zero.
In that case, tan(x) = (b - d)/(a - c)
or x = tan-1[(b - d)/(a - c)]
Wiki User
∙ 10y agoVelocity is a vector, you can sum velocity in terms of direction components such as x and y.
The vector's 'x'-component is -13.181 (rounded). Its 'y'-component is +63.649 (rounded). (I'm assuming that the angle of 101.7 is stated in units of 'degrees'.)
The magnitude of (i + 2j) is sqrt(5). The magnitude of your new vector is 2. If both vectors are in the same direction, then each component of one vector is in the same ratio to the corresponding component of the other one. The components of the known vector are 1 and 2, and its magnitude is sqrt(5). The magnitude of the new one is 2/sqrt(5) times the magnitude of the old one. So its x-component is 2/sqrt(5) times i, and its y-component is 2/sqrt(5) times 2j. The new vector is [ (2/sqrt(5))i + (4/sqrt(5))j ]. Since the components of both vectors are proportional, they're in the same direction.
If you assume the vector is only in two dimensions, you can find the missing y-component with Pythagoras' Theorem: y = square root of (magnitude2 - x2).
If I understand the question correctly, it is about the component of a vector along the axes, with the angle measured from the positive direction of the x-axis. If so, sin is used on the y-component.
To find the direction of a vector, you can use the formula: θ = tan^(-1) (y/x), where θ is the angle of the vector with the positive x-axis, and (x, y) are the components of the vector along the x and y axes, respectively.
Suppose the magnitude of the vector is V and its direction makes an angle A with the x-axis, then the x component is V*Cos(A) and the y component is V*Sin(A)
A vector can be expressed in terms of its rectangular components by breaking it down into its horizontal and vertical components. These components represent the projection of the vector onto the x and y axes. The vector can then be expressed as the sum of these components using the appropriate unit vectors (i and j for x and y directions, respectively).
Velocity is a vector, you can sum velocity in terms of direction components such as x and y.
To find the components of a vector, first determine the direction of the vector using angles or a reference axis. Then, use trigonometry (like sine and cosine functions) to calculate the components in the x and y directions.
To combine velocities in the same direction, simply add them together. For velocities in different directions, you can use vector addition to find the resultant velocity. This involves breaking the velocities into their respective x and y components and adding them separately.
To calculate a vector sum, add the corresponding components of the vectors together. This means adding the x-components to get the resultant x-component, and adding the y-components to get the resultant y-component. The magnitude of the resultant vector can be found using the Pythagorean theorem, and the direction can be determined using trigonometry.
To combine force vectors, use vector addition. Add the x-components of the forces together to get the resultant x-component, and then do the same for the y-components. The magnitude and direction of the resultant force can be found using trigonometry.
It is the other way round - it's the vector that has components.In general, a vector can have one or more components - though a vector with a single component is often called a "scalar" instead - but technically, a scalar is a special case of a vector.
A vector in space has 3 components: one for each dimension - x, y, and z. These components represent the magnitude of the vector in each respective direction.
Vectors are added by adding the components of each vector in the same direction. For example, to add two vectors in the x-direction, you add their x-components, and for the y-direction, you add their y-components. The resultant vector is then the sum of these component-wise additions.
To specify a vector quantity completely, you must state its magnitude (size), direction (specific orientation in space), and the coordinate system in which it is defined. Additionally, for 3-dimensional vectors, you may need to specify its components along the x, y, and z axes.