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10 cards from this deck
A 3D vector has components along xxx, yyy, and zzz axes.
Sum corresponding components: a+b=(ax+bx,...)a + b = (a_x+b_x,...)a+b=(ax+bx,...).
Magnitude: ∣v∣=vx2+vy2+vz2|v| = \sqrt{v_x^2 + v_y^2 + v_z^2}∣v∣=vx2+vy2+vz2.
Dot product: a⋅b=ax⋅bx+ay⋅by+az⋅bz\mathbf{a} \cdot \mathbf{b} = a_x \cdot b_x + a_y \cdot b_y + a_z \cdot b_za⋅b=ax⋅bx+ay⋅by+az⋅bz.
The cross product yields a vector perpendicular to both.
Use cosθ=a⋅b∣a∣∣b∣\cos \theta = \frac{a \cdot b}{|a| |b|}cosθ=∣a∣∣b∣a⋅b to find θ\thetaθ.
Area = ∣a×b∣|a × b|∣a×b∣, the magnitude of the cross product.
Volume = ∣a⋅(b×c)∣|a \cdot (b \times c)|∣a⋅(b×c)∣ using dot and cross products.
Unit vectors are iii, jjj, kkk along xxx, yyy, zzz axes.
v=(vx,vy,vz)=vxi+vyj+vzkv = (v_x, v_y, v_z) = v_x i + v_y j + v_z kv=(vx,vy,vz)=vxi+vyj+vzk.
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