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When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in the
same direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
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What is the angle in which the dot product of two non zero vectors is equal?
It depends on what the dot product is meant to be equal to.
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
What is the least number of non-zero vectors that can be added to give a resultant equal to zero?
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
Can three vectors of equal magnitude be combined to give a zero resultant?
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
When is the vector sum equal in magnitude to the algebraic sum?
When the angle between any two component vectors is either zero or 180 degrees.
What is the angle in which the dot product of two non zero vectors is equal?
It depends on what the dot product is meant to be equal to.
What is the angle between two vectors if their sum is to be maximum?
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
Can the resultant of two vectors be equal to zero?
Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
If two vector have equal magnitudes can their sum be zero Explain?
Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
What is the least number of non-zero vectors that can be added to give a resultant equal to zero?
Two - if you add two vectors of equal magnitude but in opposite directions, the resultant vector is zero.
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
Can three vectors of equal magnitude be combined to give a zero resultant?
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?
Two is the minimum number of vectors that will sum to zero.
Is it is possible to add three vectors of equal magnitude and get zero?
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
