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Recent questions tagged plane


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The equation of position vs. time for a moving object, in SI units, is as \(x=-t^{2}+6 t-9 .\) Which of the following choices are correct?
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If the sum of three vectors in $R^{3}$ is zero, must they lie in the same plane? Explain.
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In \(\mathbb{R}^{4}\), compute the distance from the point \((1,-2,0,3)\) to the hyperplane \(x_{1}+3 x_{2}-\) \(x_{3}+x_{4}=3\).
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In \(\mathbb{R}^{3}\), let \(N\) be a non-zero vector and \(X_{0}\) and \(Z\) points.
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In \(\mathbb{R}^{3}\), let \(N\) be a non-zero vector and \(X_{0}\) and \(Z\) points.In \(\mathbb{R}^{3}\), let \(N\) be a non-zero vector and \(X_{0}\) and \(Z\) points. a) Find the equation of the plane through the origin that is ort ...
by MathsGee Platinum
(106,962 points)
asked in Mathematics Jan 21
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Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
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Find the inverse to a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
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Find a matrix that rotates the plane through \(+60\) degrees, keeping the origin fixed.
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Find a \(2 \times 2\) matrix that reflects across the horizontal axis followed by a rotation the plane by \(+45\) degrees.
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Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees followed by a reflection across the horizontal axis.
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Find a \(2 \times 2\) matrix that rotates the plane by \(+45\) degrees \((+45\) degrees means 45 degrees counterclockwise).
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Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if \[ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \]
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How do I determine the equation of a normal in $R^2$ or $R^3$?
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How do I determine the equation of a normal in $R^2$ or $R^3$?How do I determine the equation of a normal in $R^2$ or $R^3$? ...
by MathsGee Platinum
(106,962 points)
asked in Mathematics Jan 13
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What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
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Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
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Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
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Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
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A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?

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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal toThe distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to   A) $\dfrac{1}{3}$ B) 3 C) $\dfrac{1}{15}$ D) 5 E) no ...
by MathsGee Platinum
(106,962 points)
asked in Mathematics Jan 13
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