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The cosine function is used in the scalar product (or dot product) because it quantifies the angle between two vectors. The scalar product is defined as the product of the magnitudes of the two vectors multiplied by the cosine of the angle between them. This relationship captures how aligned the vectors are: when they point in the same direction, the cosine is 1, and when they are perpendicular, the cosine is 0. Thus, using cosine allows us to measure both the magnitude and directional alignment of the vectors in the product.
What else can I help you with?
Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
Why you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
What is scalar and vector product?
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
Why scalar product are commutative?
i think that scalar product are commutative because the vectors are in the same direction
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.
Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
What is the formula of scalar?
sdsdsdsd dsdsdsdsddsdsdsds dsdsdsdsdsdsdsd
What is the product of vector and scalar?
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.
Why you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
What is scalar and vector product?
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
Why the work is scalar quantity?
Work is the product of a force and a displacement. Both of those are vectors. There are two ways to multiply vectors. One of them produces another vector, the other produces a scalar. The calculation for 'work' uses the scalar product. The procedure is: (magnitude of one vector) times (magnitude of the other vector) times (cosine of the angle between them).
Why scalar product are commutative?
i think that scalar product are commutative because the vectors are in the same direction
Can scalar product be negative?
Yes, the scalar product of two vectors can be negative if the angle between them is obtuse (greater than 90 degrees). In this case, the result of the scalar product will be negative.
Why we use sine angle in cross product while cos angle in dot product?
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
Can a scalar product be a negative quantity?
Yes, a scalar product can be negative if the angle between the two vectors is obtuse (greater than 90 degrees). The scalar product is the dot product of two vectors and is equal to the product of their magnitudes and the cosine of the angle between them. A negative scalar product indicates that the vectors are pointing in opposite directions.
Scalar or dot product?
They are the same.
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.
