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Can the resultant of two vectors be smaller than even the smaller of the two?
Wiki User
∙ 11y ago
Yes. Here is an example:
Vector A: 10 units towards the right.
Vector B: 9 units towards the left. This is the same as (-9) units to the right.
A + B: 10 + (-9) = +1 units to the right.
In fact, the resulting vector can be made arbitrarily small, if the two vectors are similar in size and point in opposite directions (or nearly so).
Wiki User
∙ 11y ago
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Can the resultant magnitude of 2 vectors be smaller than either of the vectors?
Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
What is the resultant of two vectors?
The resultant of two vectors is a third vector., for example V1 + V2 = V3. V3 may be equal to zero, greater than zero or less than zero.
Can the magnitude of a resultant vector be greater than the sum of individual vectors?
The resultant vector IS the sum of the individual vectors. Its magnitudecan be the sum of their individual magnitudes or less, but not greater.
What is the sum of two vectors called?
This is just called the "sum". Sometimes also the "resultant vector".
Can the resultant magnitude of 2 vectors be smaller than either of the vectors?
Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
What is the resultant of two vectors?
The resultant of two vectors is a third vector., for example V1 + V2 = V3. V3 may be equal to zero, greater than zero or less than zero.
Can the magnitude of a resultant vector be greater than the sum of individual vectors?
The resultant vector IS the sum of the individual vectors. Its magnitudecan be the sum of their individual magnitudes or less, but not greater.
Is it possible for two vectors that their resultant be greater than their algebric sum?
No.
What is the resultant force if the first force has an upward vector and the second force has a downward vector?
The resultant force would be the difference between the two forces, taking into account their directions. If the magnitudes of the forces are equal, the resultant force would be zero. If one force is greater than the other, the resultant force would be in the direction of the greater force.
What is the sum of two vectors called?
This is just called the "sum". Sometimes also the "resultant vector".
Can a vector have a component greater than its magnitude in higher level physics?
yeah, it can. for example consider two antiparallel vectors of magnitude 5,3 whose resultant is 2, which is smaller than both components.....
Can the magnitude of the resultant of two vector be greater than the sum of magnitudes of individual vectors?
No.
Can the magnitude of a resultant vector ever be less than the magnitude of one of its components?
Yes, if the two vectors are at a sufficiently large obtuse angle.The law of cosines gives the size of the resultant.If C = A + B, where A, B, C are vectors, then C is the "resultant."The law of cosines says, he magnitudes, A,B,C, are related as follows,C2=A2+B2+2AB cosine(theta),where theta is the angle between the vectors A and B. When theta is zero, then C has the maximum length, equal to the lengths of A and B added. When theta is 180 degrees, then C has the minimum length of the difference of the length of A and of B. Somewhere in between, the length of C will equal the length of the longer component and for larger angles be smaller.To be specific, suppose that A is the longer of the two, then the resultant, C, has the same length as A at one special angle which we will call theta*.A2=A2+B2+2AB cosine(theta*)cosine(theta*)=-B/(2A).The answer to the question is then, that for angles greater than theta* the resultant is smaller than the larger component. (Greater means, of course, greater than theta* and up to 360-theta*.)Note that if we ask whether the resultant can be smaller than the smaller of the two component vectors, then the answer is again yes and the above equation holds true when A is the smaller with the condition that it is not smaller than half the length of B. When the smaller vector is less than half the length of the larger component, then the resultant may equal the length of the larger but can never be made equal to the length of the smaller component.
What should be the angle between the two vectors of magnitudes 3.20and 5.70 units so that their resultant has a magnitudeof 10 units?
The maximum value that the combination of two vectors can have is sum of their magnitudes which in this case is 8.9. This maximum value is less than the needed 10, therefore no angle between them will produce the necessary resultant.
How can you add vectors?
To add vectors, add their corresponding components together. If the vectors are in 2D, add the x-components together and the y-components together. If they are in 3D, add the x, y, and z-components accordingly. This will result in a new vector representing the sum of the original vectors.
