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The scalar product of two perpendicular vectors is zero.
In classical mechanics we define the scalar product between two vector a and b as:
a · b = |a| |b| cos(alpha)
where |a| is the modulus of vector a and alpha is the angle between vectors a and b.
If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.
So finally a · b = 0.
The product of a vector and a scalar is a new vector whose magnitude is the product of the magnitude of the original vector and the scalar, and whose direction remains the same as the original vector if the scalar is positive or in the opposite direction if the scalar is negative.
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What is it called when a scalar and a vector are multiplied together?
When a scalar quantity(if it has positive magnitude) is multiplies by a vector quantity the product is another vector quantity with the magnitude as the product of two vectors and the direction and dimensions same as the multiplied vector quantity e.g. MOMENTUM
Is charge scalar or vector?
vector
What is speed a scalar or vector quantity?
scalar
Is torque is a scalar or a vector quantity?
Torque is a vector quantity because it has both magnitude (how strong the force is) and direction (the axis about which the force is applied).
Scalar and vector?
A scalar is a magnitude that doesn't specify a direction. A vector is a magnitude where the direction is important and is specified.
Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
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.
What is the product of two vector quantities?
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Is a scalar a component of a vector?
Answer: A vector is always the product of 2 scalars
What is scalar and vector product simplify?
Scalar product (or dot product) is the product of the magnitudes of two vectors and the cosine of the angle between them. It results in a scalar quantity. Vector product (or cross product) is the product of the magnitudes of two vectors and the sine of the angle between them, which results in a vector perpendicular to the plane containing the two original vectors.
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.
Is the cross product vector or scalar?
The cross product is a vector. It results in a new vector that is perpendicular to the two original vectors being multiplied.
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.
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 is it called when a scalar and a vector are multiplied together?
When a scalar quantity(if it has positive magnitude) is multiplies by a vector quantity the product is another vector quantity with the magnitude as the product of two vectors and the direction and dimensions same as the multiplied vector quantity e.g. MOMENTUM
Why the product of two vectors is sometime scalar and sometime vector?
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
What is a scalar times a vector?
A scalar times a vector is a vector.
