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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
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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
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
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.
Is the sum of two vectors of equal magnitude equal to the magnitude of either vectors AND their difference root 3 times the magnitude of each vector?
No, the statement is incorrect. The sum of two vectors of equal magnitude will not equal the magnitude of either vector. The sum of two vectors of equal magnitude will result in a new vector that is larger than the original vectors due to vector addition. The magnitude of the difference between the two vectors will be smaller than the magnitude of either vector.
Can the sum of two vectors be equal to either of the vectors explain?
Yes, if one of the vectors is the null vector.
What are different conditions that could make vector product zero?
The vector product (cross product) of two vectors will be zero when the vectors are parallel or antiparallel to each other. This means the vectors are either pointing in the same direction (parallel) or in opposite directions (antiparallel).
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.
If is added to under what conditions does the resultant vector have a magnitude equal to A B?
1. When the two vectors are parlell the magnitude of resultant vector R=A+B. 2. When the two vectors are having equal magnitude and they are antiparlell then R=A-A=0. For more information: thrinath_dadi@yahoo.com
Is a vector sum called the resultant.?
Yes, the vector sum is called the resultant. The resultant is the single vector that represents the combined effect of two or more vectors. It is equal to the vector sum of the individual 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 is the direction of the resultant vector after adding two equal and opposite vectors?
The resultant vector will have a magnitude of zero because the two equal and opposite vectors cancel each other out. The direction of the resultant vector will be indeterminate or undefined.
