PHYS 206 - Chapter 1: Units, Physical Quantities and Vectors

A set of practice flashcards about units, scalars vs vectors, vector notation, components, vector addition, and vector products (dot and cross) from Chapter 1.

What is the difference between a scalar and a vector?

A scalar has only magnitude (and possibly units); a vector has both magnitude and direction.

What is a unit vector?

A vector with magnitude 1 used to indicate direction; denoted with a hat (e.g., ihat, jhat, k_hat).

How is a 2D vector written in component form?

A = Ax ihat + Ay jhat; its magnitude is |A| = sqrt(Ax^2 + Ay^2).

How do you compute the magnitude of A = 2.0 ihat + 4.0 jhat?

|A| = sqrt(2.0^2 + 4.0^2) = sqrt(20) ≈ 4.47 (in the same units as Ax and Ay).

Is vector addition commutative?

Yes; A + B = B + A.

How do you add vectors component-wise?

If C = A + B, then Cx = Ax + Bx, Cy = Ay + By (Cz = Az + Bz in 3D).

What is the dot (scalar) product formula?

A · B = Ax Bx + Ay By + Az Bz = AB cos(theta).

What is the cross product and its magnitude?

A × B is a vector with magnitude |A×B| = AB sin(theta); direction is perpendicular to both or given by the right-hand rule.

How do you compute A × B using components?

A × B = (Ay Bz − Az By) ihat + (Az Bx − Ax Bz) jhat + (Ax By − Ay Bx) k_hat.

What is a unit vector along A?

A_hat = A / |A|; it points in the same direction as A and has magnitude 1.

Is ihat + jhat + k_hat a unit vector?

No; its magnitude is sqrt(3), which is greater than 1.

Can a unit vector have any component with magnitude greater than unity?

No; the components of a unit vector cannot have magnitude greater than 1 (though components can be negative).

How is a 2D vector expressed in polar form using r and theta?

A = r cos(theta) ihat + r sin(theta) jhat; r is the magnitude, theta is the angle from the +x axis.

What is dimensional analysis in physics?

Checking that the units on both sides of an equation are consistent; inconsistent units indicate an invalid equation.

How do you perform unit conversion by multiplying by 1?

Multiply by a conversion factor equal to 1, e.g., 500 miles × (1609 m / 1 mile) = 804,500 m.

What is the right-hand rule for the cross product?

Point the index finger along A, the middle finger along B, then the thumb points in the direction of A × B.