As your final answer? No. The dot product has a bunch of properties, some of which apply in this problem.spoc21 said:Homework Statement
Expand and simplify:
(2[tex]\vec{a}[/tex] + 3[tex]\vec{b}[/tex]) .(5[tex]\vec{a}[/tex] - [tex]\vec{b}[/tex]
Homework Equations
The Attempt at a Solution
I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2[tex]\vec{a}[/tex])([tex]\vec{a}[/tex]) = 2 [tex]\vec{a}[/tex]2?
Thanks..
Mark44 said:No, this is incorrect for two reasons.
a[itex]\cdot[/itex]a [itex]\neq[/itex]a2. These are vectors and they are being multiplied using the dot product. There is a property of the dot product that allows you to do something with a[itex]\cdot[/itex]a.
Also, two of your three coefficients are wrong.
This is correct.spoc21 said:I always thought that
a.a = lal2 (this isn't correct?)
OK, then the coefficients are correct, but you shouldn't write a2, b2, or ab. All of these are dot products, and you should simplify the a.a and b.b terms.spoc21 said:Two of my three coefficients are wrong? (please note that I made a mistake copying down the question in my first post, it is actually -2 a instead of 2 a). Is this correct?
Thanks..
A vector dot product, also known as a scalar product, is a mathematical operation that takes two vectors and produces a scalar quantity. It is calculated by multiplying the corresponding components of the two vectors and then adding them together.
The vector dot product is used to determine the angle between two vectors, find the projection of one vector onto another, and solve various physics and engineering problems involving forces and work.
To calculate a vector dot product, you multiply the corresponding components of the two vectors and then add them together. For example, if vector A = [a1, a2, a3] and vector B = [b1, b2, b3], their dot product would be a1b1 + a2b2 + a3b3.
A vector dot product results in a scalar quantity, while a vector cross product results in a vector quantity. The dot product is calculated by multiplying the corresponding components of two vectors and adding them, while the cross product is calculated by taking the determinant of a specific matrix composed of the two vectors.
A vector dot product can be used in various mathematical and scientific fields, such as physics, engineering, and computer graphics. It is commonly used to calculate work, power, and angles between vectors, as well as to solve force and motion problems.