BackVectors and Vector Operations in Physics
06:13
Terms in this set (20)
A vector is a quantity that has both magnitude and direction, represented by an arrow.
Scalars have only magnitude, while vectors have both magnitude and direction.
The magnitude of a vector π΄β is denoted as π΄ and equals the length of the arrow, with the same units as the vector.
By an angle π relative to the positive x-axis, measured counterclockwise (positive) or clockwise (negative).
π΄β = π΄ cos π and π΄α΅§ = π΄ sin π, valid in all four quadrants.
Use the Pythagorean theorem: \(A=\sqrt{A_x^2 + A_y^2}\).
Use the inverse tangent: \(\theta=\arctan\left(\frac{A_y}{A_x}\right)\), adjusting for quadrant.
Place the tail of one vector at the tip of another; the resultant vector goes from the tail of the first to the tip of the second.
Yes, π΄β + π΅β = π΅β + π΄β.
π΄β - π΅β = π΄β + (-π΅β), where -π΅β is the vector with the same magnitude but opposite direction as π΅β.
Add all x-components and y-components separately, then find magnitude and direction of the resultant vector.
As π΄β = A_x π€Μ + A_y π₯Μ + A_z πΜ, with components along x, y, and z axes.
Use \(A=\sqrt{A_x^2 + A_y^2 + A_z^2}\).
πβ β πβ = a_x b_x + a_y b_y + a_z b_z, resulting in a scalar.
\(\cos \theta = \frac{\mathbf{a} \cdot \mathbf{b}}{ab}\), where π is the angle between vectors.
Zero if vectors are perpendicular, positive if angle < 90Β°, negative if angle > 90Β°.
πβ = πβ Γ πβ is a vector perpendicular to both πβ and πβ, with magnitude \(c = ab \sin \theta\).
It equals the area of the parallelogram spanned by the two vectors.
When the two vectors are parallel or anti-parallel (angle 0Β° or 180Β°).
It is anticommutative: πβ Γ πβ = - πβ Γ πβ, and distributes over addition.