A vector has both magnitude (length) and direction. Written as vec{v} = langle a, b rangle or begin{pmatrix} a b end{pmatrix}. Magnitude: |vec{v}| = sqrt…
A vector has both magnitude (length) and direction. Written as vec{v} = langle a, b rangle or begin{pmatrix} a b end{pmatrix}. Magnitude: |vec{v}| = sqrt{a^2 + b^2} Operations: - Addition: langle a, b rangle + langle c, d rangle = langle a+c, b+d rangle - Subtraction: langle a, b rangle - langle c, d rangle = langle a-c, b-d rangle - Scalar multiplication: k langle a, b rangle = langle ka, kb …
Example: If vec{u} = langle 3, 4 rangle and vec{v} = langle -1, 2 rangle, find vec{u} + vec{v} and |vec{u}|.
Vector questions on the ACT are usually straightforward component arithmetic. Treat the x and y components separately — it's just two parallel calculations. The magnitude is always the Pythagorean theorem.
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