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Can the magnitude of a vector be ever equal to one of its components?
Wiki User
∙ 11y ago
Yes. - if all the other components are zero.
When the word "component" means the mutually perpendicular vectors that add (through vector addition) to form the resultant, then then answer is that "the magnitude of a vector" can equal one of its components, if and only if all other components have zero length (magnitude).
This answer applies to the typical case of a vector being expressed in terms of components defined by an orthogonal basis. In normal space, these basis vectors merely define the relevant orthogonal coordinate system. There are, however, mathematical systems that use a nonorthogonal basis and the answer is different and presumably not part of the submitted question.
Wiki User
∙ 11y ago
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Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
Can prime numbers be equal?
How can 2 prime numbers ever be equal They cant be Equal.
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.
Suppose you have two vectors that have different magnitudes can the vectors sum ever be zero?
No. The largest possible resultant magnitude is the sum of the individual magnitudes.The smallest possible resultant magnitude is the difference of the individual magnitudes.
Can the remainder ever equal the divisor?
No.
Can the component of a vector ever be greater than the magnitude of the vector?
No.
Can the magnitude of the difference between two vectors ever be greater than the magnitude of either vector?
Yes, the magnitude of the difference between two vectors can be greater than the magnitude of either vector. This can occur when the vectors are in opposite directions or have different magnitudes such that the resulting difference vector is longer than either of the original vectors.
Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?
No, the magnitude of the difference between two vectors cannot be greater than the magnitude of their sum. This is due to the triangle inequality, which states that the magnitude of the sum of two vectors is always greater than or equal to the magnitude of their difference.
Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
Can the magnitudes of the difference between two vector ever be greater than magnitude of either vector?
Yes. For example, if one vector has a length of 1 and points north, and the second vector has a length of 1 and points south, the difference (vector1 minus vector2) will have a length of 2 and point north.
Does the instantaneous speed ever equal the magnitude of its average velocity?
Yes, instantaneous speed can be equal to the magnitude of the average velocity when an object is moving in a straight line without changing its direction during the motion. This occurs at the moment when the instantaneous velocity vector is in the same direction as the average velocity vector.
What was the magnitude of the strongest earthquake ever?
9.5
What earthquake magnitude is the highest ever?
The magnitude 9.5 earthquake that occurred in Valdivia Chile in 1960.
Is there an earthquake with a 10.0 magnitude?
No there has never been an earthquake with a magnitude of 10.0 that has ever been recorded. The largest recorded to date was the magnitude 9.5 earthquake that occurred in Valdivia Chile in 1960.
What is the strongest magnitude earthquake ever measured on the Richter magnitude?
The strongest earthquake that can be measured using the Richter magnitude scale is one with a magnitude of 8.0. For earthquakes larger than this, the moment magnitude scale must be used.
Where were the 2 largest earthquakes ever?
The largest earthquake ever recorded was in Valdivia, Chile in 1960 with a magnitude of 9.5. The second largest earthquake was in Prince William Sound, Alaska in 1964 with a magnitude of 9.2.
Was there ever a magnitude ten earthquake?
No. The largest ever recorded was in 1965 in Chile and that was a 9.5.
