How do you expand a vector?

How do you expand a vector?

In Adobe Illustrator you can find it in the Menu > Object > Expand Appearance this will expand general vector attributes and effects. Then to take it further you can expand objects, fonts, fills, or strokes using Menu > Object > Expand and selecting which ones to expand.

How do you do the triple cross product?

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1. THE TRIPLE CROSS PRODUCT. A × (B × C)
2. Note that the vector G = B × C is perpendicular to the plane on which vectors B and. C lie.
3. {
4. (A · C)B − (A · B)C.
5. }
6. Selecting arbitrarily A = k, B = j, and C = k, for instance, and substituting in the above equality, one obtains λ = 1.

How do you expand the dot product of a vector?

(These properties mean that the dot product is linear.) Given these properties and the fact that the dot product is commutative, we can expand the dot product a⋅b in terms of components, a⋅b=(a1i+a2j+a3k)⋅(b1i+b2j+b3k)=a1b1i⋅i+a2b2j⋅j+a3b3k⋅k+(a1b2+a2b1)i⋅j+(a1b3+a3b1)i⋅k+(a2b3+a3b2)j⋅k.

Is vector triple product associative?

Vector triple product is not associative.

Can you expand dot product?

What is vector triple product?

Vector Triple Product is a branch in vector algebra where we deal with the cross product of three vectors. The value of the vector triple product can be found by the cross product of a vector with the cross product of the other two vectors.

What is the definition of the scalar triple product?

The definition for the scalar triple product can be explained as it is the dot product of one of the vectors with the cross product of the other two vectors. This is also termed as the box product or mixed product. It is the volume of the parallelepiped distinct by the three vectors shown.

What are the two ways of multiplying vectors?

Ans: There are two ways of multiplying vectors which can be explained as the vector product and the scalar product. The vector product has a huge application in physics and astronomy. The product of two vectors implies a vector that is perpendicular to each other.

Why do we include parentheses in a vector triple product?

For this reason it is vital that we include the parentheses in a vector triple product to indicate which vector product should be performed first. We now obtain a formula for the vector triple product which reflects the fact that u × (v × w), as it is coplanar with v and w, may be expressed as α v + β w for some α, β ∈ ℝ.