Tagged Questions

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Plane dropping a bomb vector homework problem

The following is a homework problem I want to make sure I have correct (I'll be answering): A bomber is flying at an altitude of 30,000 feet at a speed of 540 miles per hour. A bomb is released ...
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Vectors Calculation Question

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $\sqrt{A^2 + B^2 +2ABcosθ}$. Any ...
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Form a Parallelogram by 4 Points

This is a question from my school. The following is the whole question. The vertices of a triangle A, B and C are given by the points (-1, 0, 2), (0, 1, 0), (1, -1, 0) respectively. Find ...
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Vector calculus: Arclength

Please help. I need a guide for this homework question. Let $u_1 = (x+y)/2$ and $u_2 = (x-y)/2$, where $x$ and $y$ are Cartesian coordinates. Write the differential $d \vec{r}$ as a linear ...
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Confusion regarding orientation of curves in Green's Theorem

I am in the middle of helping some friends out with their vector calculus assignment (I don't do this course). Now in their assignment they have the following question: Consider the integral ...
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Vector derivation of $x^Tx$

Let $x \in \mathbb{R}^n$ What is $$\frac{\partial}{\partial x} [ x^Tx ]$$ My guess is: $\frac{\partial}{\partial x} [ x^Tx ] = 0$, because $[x^Tx] \in \mathbb{R}^1$, hence a real number as is ...
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Vector derivatives, what is the minimum of this matrix equation?

I am new to vector derivatives and trying to figure out a lot for my Machine Learning course. I have given the following: $x \in \mathbb{R}^n$, $y \in \mathbb{R}^d$, $A \in \mathbb{R}^{d \times n}$, ...
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Fleming's “right-hand rule” and cross-product of two vectors

I have been throwing around hand gestures for the past hour in a feeble attempt at trying to solve this question involving a cross product of two vectors $a$ x $b$. So far, I haven't found any ...
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how do I calculate Hessian of this function?

I have a function $f(x) = (\mathbf x ^ \top \mathbf x) ^ {p/2}$. Its gradient is $\nabla f(x) = 2p (\mathbf x ^ \top \mathbf x) ^ {(p-2)/2} \mathbf x$ How do I compute its Hessian $\nabla^2f(x)$? ...
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Three-dimensional vectors and force systems

Full disclosure: this is a homework problem. However, I find myself stuck in the middle. The problem is below As shown, a system of cables suspends a crate weighing W = 350 . (Part C 1 figure) ...
Example of a vector norm for which $\|I\|<1$
In order to prove a larger assumption, I need to find a vector norm over $M_n$ such that $\|I\| < 1$. None of the standard $p$-norms, nor the infinity norm work. I know that for matrix norms, ...
I'm trying to show that a vector norm $\|\cdot\|$ being absolute ($\|x\| = \|\;|x|\;\|)$ is equivalent to showing that $\|x'\| = \|[\alpha_1x_1\ldots\alpha_nx_n]^T\| = \|x\|$ for all ...