Dot Products of Vectors
Read this topicExplanations 4
- It turns out that the dot product is equal to the product of the magnitudes of the vectors times the cosine of the angle between the vectors (a⃗⋅b⃗=∣∣a⃗∣∣⋅∣∣b⃗∣∣cosα\vec{a}\cdo…
By Wayne Zhao, Anusha Rahman
- (Video) The Dot Product by PatrickJMT Here's a video by patrickJMT showing you how to find the dot product of two vectors.
By Alex Federspiel, Anusha Rahman
- Mathematicians have a nasty habit of asking questions by stringing together words and hoping they can somehow be interpreted. So it was with the dot product. The dot product was…
By Wayne Zhao, Alex Federspiel, Gabi Slizewska
- Vector Dot Product The vector dot product allows us to multiply two vector quantities together, giving us a scalar quantity (or scalar product). There are two ways that we can f…
By Anusha Rahman
Problems 20
- Let x⃗,y⃗\vec{x}, \vec{y}x,y be column vectors of length 333 and z⃗\vec{z}z be a row vector of length 333. Let AAA be an 3×33\times 33×3 matrix. Which of the following are vali…
- Let x⃗=[305−2]\vec{x} = \begin{bmatrix} 3 \\ 0 \\ 5 \\ -2 \end{bmatrix}x=305−2 and y⃗=[610−12]\vec{y} = \begin{bmatrix} 6 \\ 10 \\ -1 \\ 2 \end{bmatrix}y=610−12. What is …
- Let xxx be a real number such that [x36]⋅[2x3x]=5\begin{bmatrix} x \\ 3 \\ 6 \end{bmatrix} \cdot \begin{bmatrix} 2x \\ 3 \\ x \end{bmatrix} = 5x36⋅2x3x=5 Which of the foll…
- Let x⃗=[960]\vec{x} = \begin{bmatrix} 9 \\ 6 \\ 0 \end{bmatrix}x=960 and y⃗=[611]\vec{y} = \begin{bmatrix} 6 \\ 1 \\ 1 \end{bmatrix}y=611. What is x⃗⋅y⃗\vec{x} \cdot \vec…
- Let x⃗=[−2−3−7]\vec{x} = \begin{bmatrix} -2 \\ -3 \\ -7 \end{bmatrix}x=−2−3−7 and y⃗=[82−3]\vec{y} = \begin{bmatrix} 8 \\ 2 \\ -3 \end{bmatrix}y=82−3. What is x⃗⋅y⃗\vec{x…
- Let x⃗=[x11x]\vec{x} = \begin{bmatrix} x \\ 1 \\ \frac1x \end{bmatrix}x=x1x1 and y⃗=[37−x]\vec{y} = \begin{bmatrix} 3 \\ 7 \\ -x \end{bmatrix}y=37−x. What is xxx if x⃗⋅y…
- Let x⃗=[525]\vec{x} = \begin{bmatrix} 5 \\ 2 \\ 5 \end{bmatrix}x=525 and y⃗=[9423]\vec{y} = \begin{bmatrix} 9 \\ 4 \\ 23 \end{bmatrix}y=9423. What is x⃗⋅y⃗\vec{x} \cdot \…
- Let x⃗=[54203]\vec{x} = \begin{bmatrix} 5 \\ 42 \\ 0 \\3 \end{bmatrix}x=54203 and y⃗=[51341]\vec{y} = \begin{bmatrix} 5 \\ 1 \\ 34 \\ 1 \end{bmatrix}y=51341. What is x⃗⋅y…
- Let x⃗=[120302]\vec{x} = \begin{bmatrix} 1 \\ 20 \\ 3 \\ 0 \\2 \end{bmatrix}x=120302 and y⃗=[64107]\vec{y} = \begin{bmatrix} 6 \\ 4 \\ 1 \\0 \\7 \end{bmatrix}y=64107. Wha…
- Let x⃗=[862143]\vec{x} = \begin{bmatrix} 86 \\ 21 \\ 43 \end{bmatrix}x=862143 and y⃗=[310]\vec{y} = \begin{bmatrix} 3 \\ 1 \\ 0\end{bmatrix}y=310. What is x⃗⋅y⃗\vec{x} \c…
- Let x⃗=[271]\vec{x} = \begin{bmatrix} 2 \\ 7 \\ 1 \end{bmatrix}x=271 and y⃗=[5406]\vec{y} = \begin{bmatrix} 5 \\ 40 \\ 6 \end{bmatrix}y=5406. What is x⃗⋅y⃗\vec{x} \cdot \…
- Let x⃗=[02]\vec{x} = \begin{bmatrix} 0 \\ 2 \end{bmatrix}x=[02] and y⃗=[37]\vec{y} = \begin{bmatrix} 3 \\ 7 \end{bmatrix}y=[37]. What is x⃗⋅y⃗\vec{x} \cdot \vec{y}x⋅y?
- Let x⃗=[355]\vec{x} = \begin{bmatrix} 3 \\ 5 \\ 5 \end{bmatrix}x=355 and y⃗=[141]\vec{y} = \begin{bmatrix} 1 \\ 4 \\ 1 \end{bmatrix}y=141. What is x⃗⋅y⃗\vec{x} \cdot \vec…
- Let x⃗=[021]\vec{x} = \begin{bmatrix} 0 \\ 2 \\ 1 \end{bmatrix}x=021 and y⃗=[492221]\vec{y} = \begin{bmatrix} 49 \\ 22 \\ 21 \end{bmatrix}y=492221. What is x⃗⋅y⃗\vec{x} \…
- Let x⃗=[5521]\vec{x} = \begin{bmatrix} 5 \\ 52 \\ 1 \end{bmatrix}x=5521 and y⃗=[402]\vec{y} = \begin{bmatrix} 4 \\ 0 \\ 2\end{bmatrix}y=402. What is x⃗⋅y⃗\vec{x} \cdot \v…
- Let x⃗=[170533]\vec{x} = \begin{bmatrix} 1 \\ 70 \\ 533 \end{bmatrix}x=170533 and y⃗=[43240]\vec{y} = \begin{bmatrix} 432 \\ 4 \\ 0 \end{bmatrix}y=43240. What is x⃗⋅y⃗\ve…
- Let x⃗=[43251]\vec{x} = \begin{bmatrix} 43 \\ 2 \\ 51 \end{bmatrix}x=43251 and y⃗=[0332]\vec{y} = \begin{bmatrix} 0 \\ 33 \\ 2 \end{bmatrix}y=0332. What is x⃗⋅y⃗\vec{x} \…
- Let x⃗=[2350]\vec{x} = \begin{bmatrix} 2 \\ 3 \\ 5 \\0\end{bmatrix}x=2350 and y⃗=[9414]\vec{y} = \begin{bmatrix} 9 \\ 4 \\ 1 \\ 4\end{bmatrix}y=9414. What is x⃗⋅y⃗\vec{x}…
- Let x⃗=[52]\vec{x} = \begin{bmatrix} 5 \\ 2 \end{bmatrix}x=[52] and y⃗=[84]\vec{y} = \begin{bmatrix} 8 \\ 4 \end{bmatrix}y=[84]. What is x⃗⋅y⃗\vec{x} \cdot \vec{y}x⋅y?
- Let x⃗=[155]\vec{x} = \begin{bmatrix} 1 \\ 5 \\ 5 \end{bmatrix}x=155 and y⃗=[942]\vec{y} = \begin{bmatrix} 9 \\ 4 \\ 2 \end{bmatrix}y=942. What is x⃗⋅y⃗\vec{x} \cdot \vec…