University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

406

Pages:

2
Author:

Niklas

IV. Vectors OPERATIONS (Ch. 6) I. VECTOR ADDITION/SUBTRACTION ↳ combine vectors by adding them. the result of vector addition is the resultant. graphical representation: ADDITION SUBTRACTION let u = (u₁, u₂) and let v = (v₁, v₂) and II SCALAR MULTIPLICATION: ↳ changes the scale of the vector and the result is a vector ↳ the scalar multiple of k times u is the vector ku = k(u₁, u₂) = (ku₁, ku₂) 4 20 シ III. PROPERTIES OF VECTOR ADDITION AND SCALAR MULTIPLICATION let u, v, w be vectors and let c and d be scalars c(du) = (cd)u (u + v) + w = u + (v + w) cu + cv (c + d)u = cu + du A- A IV. DOT PRODUCT unlike scalar multiplication, the dot product is multiplying two vectors together, and it yields a scalar definition the dot product is multiplying two vectors together, properties let u, v, w be vectors and let C be a scalar [\vec{0}\cdot\vec{v}=0] IAA-A (vw)นีพี (\langle4,5\rangle\cdot\langle2,3\rangle) 2. (2,-1) (1,2) 3. (\langle0,3\rangle\cdot\langle4,-2\rangle) [=4(2)+5(3)] [=2(1)\cdot(-1)(2)] [=0(4)+3(-2)] 23 2-2 =0 ↳ angle between two vectors cos 스 4. find & between \(\vec{u}=\langle4,3\rangle\) and \(\vec{v}=\langle3,5\rangle^{2}\) \[cos~\theta=\frac{\langle4,3\rangle\cdot\langle3,5\rangle}{||\langle4,3\rangle||||\langle3,5\rangle||}=\frac{4(3)*3(5)}{\sqrt{4^{2}+3^{2}\sqrt{3\cdot5^{2}}}\] \[cos\theta+\frac{27}{5\sqrt{34}}\] 022.17 vectors are orthogonal (at right angles) when their dot product equals O.