0
Will a vector multiplied by another vector result in another vector?
Wiki User
∙ 15y ago
It depends on the angle between the vectors (AB). The product of two vectors Av and Bv is AvBv=-Av.Bv + AvxBv= |AvBv|(-cos(Ab) + vsin(AB)). If the angle is a odd multiple of 90 degrees the product is a vector. If he angle is an even multiple of 90 degrees, the product is a scalar. If he angle is not a multiple of 90 degrees, the product of a vector by another vector is a quaternion, the sum of a scalar and a vector. Most numbers in physics and science are quaternions, a combination of scalars and vectors.Quaternions forma mathematical Group, vectors don't. The product of quaternions is always a quaternion. The product of vectors may not be a vector, it may be a vector , a scalar or both. The product of scalars is also a Group. Vector by themselves do not form a Group. The Order of Numbers are Scalars form a Group called Real Numbers; scalars and a single vector form a group called complex numbers; scalars and three vectors form a group called Quaternions. These are the only Groups that provide an Associative Division Algebra.
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
What is the result of adding a displacement vector to an another displacement vector?
another displacement
What is the result if you subtract a velocity vector to another velocity vector?
The result will also be a velocity vector. Draw the first vector. From its tip draw the negative of the second vector ( ie a vector with the same magnitude but opposite direction). The the resultant would be the vector with the same starting point as the first vector and the same endpoint as the second. If the two vectors are equal but opposite, you end up with the null velocity vector.
Why work is scalar but product of two vector?
The product of two vectors can be done in two different ways. The result of one way is another vector. The result of the other way is a scalar ... that's why that method is called the "scalar product". The way it's done is (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
What will be the change if a vector is multiplied by -2?
It will be twice as large as the original and have the opposite direction.
Can a 3 X 4 matrix be multiplied by a 4 X 1 matrix?
Yes. If one matrix is p*q and another is r*s then they can be multiplied if and only if q = r and, in that case, the result is a p*s matrix.
What is the physical significance of null vectors?
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
What is a vector times iteself?
When a vector is multiplied by itself, it is known as the dot product. The result is a scalar quantity, which represents the projection of one vector onto the other. This operation is different from vector multiplication, where the result is a new vector.
What is the result of adding a displacement vector to an another displacement vector?
another displacement
Why vector division is not possible?
In the case of the dot product, you would need to find a vector which, multiplied by another vector, gives a certain real number. This vector is not uniquely defined; several different vectors could be used to give the same result, even if the other vector is specified. For the other two common multiplications defined for vector, the inverse of multiplication, i.e. the division, can be clearly defined.
Can vector quantity be divided and multiplied?
Vector quantities can be added and subtracted using vector addition, but they cannot be divided like scalar quantities. However, vectors can be multiplied in two ways: by scalar multiplication, where a scalar quantity is multiplied by the vector to change its magnitude, or by vector multiplication, which includes dot product and cross product operations that result in a scalar or vector output.
When we subtract a velocity vector from another velocity vector the result is?
The result of subtracting one velocity vector from another velocity vector is a new velocity vector. This new vector represents the difference in speed and direction between the two original velocity vectors.
When you add a displacement vector to another displacement vector the result is?
The result is a new displacement vector that is found by adding the components of the two original vectors.
Multiplying or dividing vectors by scalars results in what?
When multiplying a vector by a scalar, each component of the vector is multiplied by the scalar. This operation changes the magnitude of the vector but not its direction. Similarly, dividing a vector by a scalar involves dividing each component of the vector by the scalar.
How will you multiply a vector by positive number?
A positive scalar multiplied by a vector, will only change the vector's magnitude, not the direction. A negative scalar multiplied by the vector will reverse the direction by 180°.
Can a scalar quantity be the product of 2 vector quantities?
No, a scalar quantity cannot be the product of two vector quantities. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. When two vectors are multiplied, the result is a vector, not a scalar.
When a vector acting 90 degree and multiply by negative number the result vector acting at?
When a vector is multiplied by a negative number, it changes direction by 180 degrees but keeps the same magnitude. Therefore, a vector initially acting at 90 degrees would end up acting at 270 degrees (or -90 degrees) after being multiplied by a negative number.
When does the vector duplicates?
When it is multiplied by 2.
