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Gurasees
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Can we find the angle between resultant and one of its vectors without breaking into components?
Gurasees said:Can we find the angle between resultant and one of its vectors without breaking into components?
How are the vectors given, if not as components? How many vectors are added to get the resultant vector?Gurasees said:Can we find the angle between resultant and one of its vectors without breaking into components?
Mathematically yes, since the angle between the vectors A and B is given by [itex]\cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert} [/itex]. Calculating the inner product of two vectors is left as an assignment for the student.Gurasees said:Can we find the angle between resultant and one of its vectors without breaking into components?
Thank yousophiecentaur said:You have to use some co ordinate system but Cartesian is not necessary. Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don't have to use components. But 20 million flies can't be wrong and using components is usually the most convenient way.
Thank youSvein said:Mathematically yes, since the angle between the vectors A and B is given by [itex]\cos(\phi)=\frac{\vec{A}\cdot \vec{B}}{\vert \vec{A}\vert\vert \vec{B}\vert} [/itex]. Calculating the inner product of two vectors is left as an assignment for the student.
The angle between resultant and vector is the angle formed between the resultant of two or more vectors and one of the vectors that make up the resultant.
The angle between resultant and vector can be calculated using the dot product or the cross product of the two vectors. The angle can also be found using trigonometric functions such as cosine or sine.
The range of values for the angle between resultant and vector is between 0 and 180 degrees, or between 0 and π radians. This is because the angle can be acute, right, or obtuse.
The angle between resultant and vector does not affect the magnitude of the resultant. The magnitude of the resultant is only affected by the magnitudes of the vectors that make up the resultant.
The angle between resultant and vector is important in vector addition as it determines the direction of the resultant vector. The angle can also help determine whether the resultant vector is maximized or minimized, depending on the angle's value.