0
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
Wiki User
∙ 14y ago
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
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 the sum of two vectors be equal to either of the vectors explain?
Yes, if one of the vectors is the null vector.
F equals ma is cross product?
No. ' a ' (acceleration) is a vector, but ' m ' (mass) is a scalar.So ' F ' (force) is a vector parallel to ' a ', with magnitude equal to the product ( m |a| ).
The vector sum of three vectors gives a resultant equal to zero What can you say about the vectors?
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
What are unit vectors?
a unit vector is a vector which has exact same direction and has its length or magnitude equal to one
How does the magnitude of a vector relate to the dot product?
The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first. for ex.- A.B=ABcos@
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 the sum of two vectors be equal to either of the vectors explain?
Yes, if one of the vectors is the null vector.
F equals ma is cross product?
No. ' a ' (acceleration) is a vector, but ' m ' (mass) is a scalar.So ' F ' (force) is a vector parallel to ' a ', with magnitude equal to the product ( m |a| ).
The vector sum of three vectors gives a resultant equal to zero What can you say about the vectors?
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
What are unit vectors?
a unit vector is a vector which has exact same direction and has its length or magnitude equal to one
What are equal vector?
If both magnitude and direction are the same then the two vectors are said to be equal.
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.
Can two vectors of unequal magnitude add up to give the zero vector?
No. The vector resultant of addition of vectors is the vector that would connect the tail of the first vector to the head of the last. For any set of vectors to add to the zero vector, the endpoint of the last vector added must be coincident with the start point of the first. Therefore for the sum of only two vectors to have a chance of being the zero vector, the second vector must be in a direction exactly opposite the first. So you can tell that the result of adding the two vectors could only can be zero vector if the two vectors were of two equal magnitude.
When the angle between two vectors is equal to zero?
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
The sum of two or more vectors is called a blank vector?
The two vectors are P & Q..Sum of the two vecotors is P+Q=R..R Is called the resultant vector of this two vector..the action of the resultant vector R is equal to the actions of two vectors P & Q..
