You haven't told us what a1, a2, and a3 are, nor have you said what "x hat" and the other two hats represent.bossman007 said:Homework Statement
A is a vector
Show that: a1 = x hat (dot) A
a2 = y hat (dot) A
a3 = z hat (dot)A
Is this given? If so, you need to say so.bossman007 said:Homework Equations
A= (a1*x hat) + a2*y hat) + (a3* z hat)
bossman007 said:The Attempt at a Solution
my hint says to take the dot product of both sides of the equation in (2) with each of the basis vectors in turn.
Doing this I get A^2 = [(a1*x hat) + a2*y hat) + (a3* z hat)] dot A
I don't know what to do next, or if that's even right.
Vector components are the individual parts that make up a vector. They are typically represented by the x and y axes in a two-dimensional coordinate system, or by the x, y, and z axes in a three-dimensional coordinate system.
The magnitude of a vector can be found using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components.
The direction of a vector is typically represented by an angle, which can be calculated using the inverse tangent function. The formula is tan-1 (opposite/adjacent), where "opposite" is the y component and "adjacent" is the x component.
To prove that two vectors are orthogonal (perpendicular), you can use the dot product method. If the dot product of two vectors is equal to 0, then they are orthogonal. The dot product is calculated by multiplying the corresponding components of the vectors and then adding them together.
Yes, vector components can be negative. This typically occurs when the vector is pointing in the direction opposite to the positive axis. It is important to pay attention to the signs of vector components when performing calculations involving vectors.