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1answer
30 views

Cross Product in 3D

Hi! I am currently working on some calc2 online homework problems concerning the cross product. I understand how the cross product works, but I am not sure how to apply it to this question. I know ...
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1answer
57 views

Prove that $g(t) \times \frac{d}{dt} g(t) = 0$

If the vectorial function $r = g(t)$, with values in $\mathbb R^3$ and where $t\in\mathbb R$, is a solution of the differential equation $\frac{d^2}{dt^2} r(t) = t^2 r(t)$, such that $g(0) = 0$, ...
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2answers
302 views

Equation of plane that goes for intersection of 2 planes and is perpindicular to another plane

Really don't know what to do here, went to a tutor neither did he. Okay first the problem: Find the equation of the plane that passes through the line of intersection of the planes x − z = 2 and y + ...
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0answers
42 views

Given the normal vector n(s), determines the curvature k(s) and the torsion

Given the normal vector n(s) of a curve $\alpha$, with non zero torsion everywhere, determines the curvature k(s) and the torsion $\tau$(s) of $\alpha$. I am first trying to show the following which ...
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votes
2answers
48 views

Prove that vectors x,y are linearly dependent exactly when …

Prove that vectors $\vec{x},\vec{y}$ (belonging to $\mathbb{R}^3$) are linearly dependent only if the following is true $$ \begin{vmatrix} x_1&y_1 \\ x_2&y_2 \end{vmatrix} ...
1
vote
3answers
89 views

How do I plot a bunch of vectors in Maple and find the difference and cross product between them?

Title says it all. This is the assignment I'm trying to do. http://math.rutgers.edu/~shtelen/Teaching/Fall-2013/L1_instr.pdf Data I need to plot ...
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1answer
93 views

Cross product as factor in dot product [duplicate]

Given there are two vectors $w,v$ with $||w||=4$ , $||v||=1$ and $\phi=\frac{2\pi}{3}$ How do you transform the following expression into a form in which it can be computed with the given ...
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2answers
69 views

Computing cross product using norm and angle

Sorry for the weird title, if someone finds a better title for my problem be my guest to edit it ;) For $\mathbf{v,w} $ in R³ with $\mathbf{||v||=1 ;||w||=4; \theta =\frac{2\pi}{3}}$ Solve ...
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1answer
45 views

Find vectors vertical to given vectors with certain length

Given the vectors $\mathbf{u,v}$ in R³, determine all vectors that are vertical to $\mathbf{u}$ and $\mathbf{v}$ with length = 1 Every vector $\mathbf{x'}$ that is to be found must meet these ...
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1answer
385 views

The Darboux vector is defined by $D = \tau T + \kappa B$. Show that $T' = D \times T$

The Darboux Vector is defined as $D = \tau T + \kappa B$. Show that for a unit speed curve $$T' = D \times T \hspace{1cm} ... $$ Here, the $...$ represents the fact that there are a few ...
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votes
1answer
777 views

invariance of cross product under coordinates rotation

Question goes as If $\vec A$ and $\vec B$ are invariant under rotation, the prove that $ \vec A \times \vec B $ is also invariant. However solution of on the other page is not given. Says ...
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1answer
5k views

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 ...