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What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
1 1 Check whether the following set of vectors is LD or LI?
(i) They are linearly dependent since the 2nd vector is twice the 1st vector. All 3 vectors lie in the x-z plane, so they don't span 3D space. (ii) They are linearly independent. Note that the cross-product of the first two is (-1,1,1). If the third vector is not perpendicular to the above cross-product, then the third vector does not lie in the plane defined by the first two vectors. (-1,1,1) "dot" (1,1,-1) = -1+1-1 = -1, not zero, so 3rd vector is not perpendicular to the cross product of the other two.
What does the x stand for in maths?
At the lower levels it stands for multiplication, at more advanced levels it stands for the cross product of vector multiplication (in three or seven dimensions). The multiplication operator can also be a dot on the line ( . ), a dot above the line ( 𝆴 ), an asterisk ( * ), and probably some other symbols as well.
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
in what components dot and cross product resolve?
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.
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 gradient of a dot product and how is it calculated?
The gradient of a dot product is a vector that represents the rate of change of the dot product with respect to each variable. It is calculated by taking the derivative of the dot product with respect to each variable and combining them into a vector.
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@
What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
What is the relationship between the gradient dot product and vector calculus?
The gradient dot product is a key concept in vector calculus. It involves taking the dot product of the gradient operator with a vector field. This operation helps in understanding the rate of change of a scalar field in a given direction. In vector calculus, the gradient dot product is used to calculate directional derivatives and study the behavior of vector fields in three-dimensional space.
Where is the resultant vector lies when dot product of two vector is done?
arithmetic mean
Is triple dot product defined?
If by "triple dot product" you mean u·v·w, then no, because that would imply the existence of a dot product between a vector and 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 work is the vector product of force and distance?
Yes and no. It's the dot product, but not the cross product.
How to find the dot product of two vectors?
To find the dot product of two vectors, you multiply the corresponding components of the vectors and then add the results together. This gives you a single scalar value that represents the magnitude of the projection of one vector onto the other.
How to perform the dot product of two vectors?
To perform the dot product of two vectors, you multiply the corresponding components of the vectors and then add the results together. This gives you a single scalar value that represents the magnitude of the projection of one vector onto the other.
