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How does the angle vectors affect the resultant vector?
The angle between two vectors significantly influences the magnitude and direction of the resultant vector. When two vectors are aligned in the same direction, their magnitudes simply add up, resulting in a larger resultant vector. Conversely, if they are at an angle to each other, the resultant vector's magnitude can be calculated using the cosine rule, and its direction is determined by the vector addition process. The greater the angle between the vectors, the more the resultant vector's magnitude can be diminished.
Define the angle of the resultant vector?
The resultant vector is the vector that 'results' from adding two or more vectors together. This vector will create some angle with the x -axis and this is the angle of the resultant vector.
What is parallelogram law of vector addition?
The parallelogram law of vector addition states that if two vectors are represented as two adjacent sides of a parallelogram, the resultant vector can be obtained by drawing a diagonal from the point where the two vectors originate. Mathematically, this law can be expressed as ( R^2 = A^2 + B^2 + 2AB \cos(\theta) ), where ( R ) is the magnitude of the resultant vector, ( A ) and ( B ) are the magnitudes of the two vectors, and ( \theta ) is the angle between them. This law illustrates how vectors can be combined geometrically and is fundamental in understanding vector addition in physics and mathematics.
In a 2 - dimensional cartesian coordinate system the y-component of a given vector is equal to the vector magnitude multiplied by which trigonometric function with respect to the angle between vector?
I disagree with the last response. It is implied that the angle you are speaking of is the angle between the x-axis and the vector (this conventionally where the angle of a vector is always measured from). The function you are asking about is the sine function. previous answer: This question is incorrect, first of all you have to tell the angle between vector and what other thing is formed?
What will be the angle if the vector have equal magnitude?
The angle can have any value.
Define the angle of the resultant vector?
The resultant vector is the vector that 'results' from adding two or more vectors together. This vector will create some angle with the x -axis and this is the angle of the resultant vector.
Two or more velocities can be combined by?
Two or more velocities can be combined by vector addition. To add velocities, the direction and magnitude of each velocity must be taken into account. The result will be a new velocity that represents the combined effect of the individual velocities.
Is there any change in the vector if there is change in angle?
Yes. The angle is the direction of the vector, so if the angle changes, the direction changes.
Is angle scalar or vector?
Almost all of us would say that angle is a scalar quantity. But the beauty is that angle is a vector quantity. Now the question arises. Where will be the direction? As we measure the angle in a plane in counter clockwise direction, then direction of angle vector will be perpendicular to the plane and coming out of the surface. If the angle is measured in clockwise then vector would go into the surface normally. As angle becomes vector then angular velocity w = @/t also becomes a vector.
Is the magnitude of a vector the same as the angle formed by the vector?
No, the magnitude of a vector is the length of the vector, while the angle formed by a vector is the direction in which the vector points relative to a reference axis. These are separate properties of a vector that describe different aspects of its characteristics.
Is angle scalar quantity or vector quantity?
Almost all of us would say that angle is a scalar quantity. But the beauty is that angle is a vector quantity. Now the question arises. Where will be the direction? As we measure the angle in a plane in counter clockwise direction, then direction of angle vector will be perpendicular to the plane and coming out of the surface. If the angle is measured in clockwise then vector would go into the surface normally. As angle becomes vector then angular velocity w = @/t also becomes a vector.
How to find the direction of a vector?
To find the direction of a vector, you can use trigonometry. First, calculate the angle the vector makes with the positive x-axis. This angle is called the direction angle. You can use the arctangent function to find this angle. The direction of the vector is then given by the direction angle measured counterclockwise from the positive x-axis.
What is the angle addition property?
If an angle has been bisected by a ray then it's now 3 angles ( the original 1, and the two created by the ray) this property says you can add the measurements of the two angles together to get the measurement of the original angle
In a 2 - dimensional cartesian coordinate system the y-component of a given vector is equal to the vector magnitude multiplied by which trigonometric function with respect to the angle between vector?
I disagree with the last response. It is implied that the angle you are speaking of is the angle between the x-axis and the vector (this conventionally where the angle of a vector is always measured from). The function you are asking about is the sine function. previous answer: This question is incorrect, first of all you have to tell the angle between vector and what other thing is formed?
What will be the angle if the vector have equal magnitude?
The angle can have any value.
What is the angle between vector a and vector b when mode of vector a plus vector b is equal to mode of vector a minus vector b?
90 degrees
Will a vector multiplied by another vector result in another vector?
It depends on the angle between the vectors (AB). The product of two vectors Av and Bv is AvBv=-Av.Bv + AvxBv= |AvBv|(-cos(Ab) + vsin(AB)). If the angle is a odd multiple of 90 degrees the product is a vector. If he angle is an even multiple of 90 degrees, the product is a scalar. If he angle is not a multiple of 90 degrees, the product of a vector by another vector is a quaternion, the sum of a scalar and a vector. Most numbers in physics and science are quaternions, a combination of scalars and vectors.Quaternions forma mathematical Group, vectors don't. The product of quaternions is always a quaternion. The product of vectors may not be a vector, it may be a vector , a scalar or both. The product of scalars is also a Group. Vector by themselves do not form a Group. The Order of Numbers are Scalars form a Group called Real Numbers; scalars and a single vector form a group called complex numbers; scalars and three vectors form a group called Quaternions. These are the only Groups that provide an Associative Division Algebra.
