Can the dot product be negative if yes what must be the condition?

Yes. When the angular width between two non-zero vectors is more than 90 degree their dot product becomes negative.

Can the dot product be negative?

Answer: The dot product can be any real value, including negative and zero. The dot product is 0 only if the vectors are orthogonal (form a right angle).

What does it mean for a dot product to be negative?

If the dot product is negative then the angle is greater than 90 degrees and one vector has a component in the opposite direction of the other. Thus the simple sign of the dot product gives information about the geometric relationship of the two vectors.

Can the scalar product of two vectors be negative if yes then for which angles?

If the angle between two vectors is acute, then their scalar product (also called dot product and inner product) is positive. If the angle between two vectors is right, then their scalar product is zero. If the angle between two vectors is obtuse, then their scalar product is negative.

Can a scalar quantity be negative?

Any scalars that are defined as the magnitude of a vector is non-negative. But, there are some scalars that can be negative. Electric charge is one of the examples of scalars that can take negative values.

What happens when a vector is negative?

vectors. … except that multiplying by a negative number will reverse the direction of the vector’s arrow. For example, multiplying a vector by 1/2 will result in a vector half as long in the same direction, while multiplying a vector by −2 will result in a vector twice as long but pointed…

Can a scalar product of two vectors be negative explain?

If one of them is negative, the scalar product can be negative. Now the cosine value can be negative; for example cos180° is -1. Therefore, in case the angle between the two vectors is 180°, the product is negative.

Can the scalar product of two vectors can be negative?

If the angle between two vectors is acute, then their scalar product (also called dot product and inner product) is positive. If the angle between two vectors is obtuse, then their scalar product is negative.

Can a scalar of two vector be negative?

Yes, it will be negative if the angle between the two vectors lies between 90° to 270°.

Can a scalar product of two vectors be negative proof with an example?

If the angle between two vectors is right, then their scalar product is zero. If the angle between two vectors is obtuse, then their scalar product is negative. Yes. It can be negative.

Does dot product obey commutative law?

Scalar multiplication of two vectors (to give the so-called dot product) is commutative (i.e., a·b = b·a), but vector multiplication (to give the cross product) is not (i.e., a × b = −b × a). The commutative law does not necessarily hold for multiplication of conditionally convergent series.

Under what conditions the scalar product of two vectors is maximum?

As one vector approaches the other one’s trajectory, the scalar product increases. Therefore, at angle 0, the scalar product is at its maximum.

Can the scalar product of two vectors be zero?

If two vectors are perpendicular to each other, their scalar product will be zero.

Why is a dot B dot C meaningless?

a) The expression ( a â‹… b ) â‹… c has meaningless because, it is the dot product of a scalar a â‹… b and a vector c. Note that here, the dot product a â‹… b is a scalar, and c is a vector, and a scalar and a vector cannot be dot product with each other.

What is dot product properties?

Dot Product Properties of Vector:

Property 1: Dot product of two vectors is commutative i.e. a.b = b.a = ab cos θ. Property 2: If a.b = 0 then it can be clearly seen that either b or a is zero or cos θ = 0. ⇒ θ = π 2.

Which of the following is obeyed by dot product?

Answer: COMMUTATIVE LAW FOR DOT PRODUCT.

How do you know if a vector is meaningless?

Which among the following vector operations are meaningless?

Clearly, →a×(→b. →c) is meaningless.

Which among the vector operation is meaningless?

Cross product of a scaler and a vector is not defined or meaningless.

How do you tell if an expression is a vector or scalar?

A vector quantity has a direction and a magnitude, while a scalar has only a magnitude. You can tell if a quantity is a vector by whether or not it has a direction associated with it. Example: Speed is a scalar quantity, but velocity is a vector that specifies both a direction as well as a magnitude.

What happens when you multiply two vectors?

Multiplication of a vector by a scalar changes the magnitude of the vector, but leaves its direction unchanged. The scalar changes the size of the vector.

Are vector vectors meaningful?

vector/scalar is a meaningful term. Force is a vector quantity while area is a scalar quantity. Hence, the correct option is (d).