For homework, I need to find the reflection of the vector <1,1,1> over the line defined by all the scalar multiples of <2,1,2>. I tried looking at the other questions about similar topics here, but they didn't help me. Could anyone give me a hint on how I am supposed to do this?
2026-03-26 09:39:49.1774517989
Reflection of a vector across a line
6.4k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in TRANSFORMATION
- $\int \ x\sqrt{1-x^2}\,dx$, by the substitution $x= \cos t$
- Functions on $\mathbb{R}^n$ commuting with orthogonal transformations
- How do you prove that an image preserving barycentric coordinates w.r.t two triangles is an affine transformation?
- Non-logarithmic bijective function from $\mathbb{R}^+$ into $\mathbb{R}$
- Where does this "magical" transformatiom come from?
- Calculate the convolution: $\frac{\sin(4t)}{\pi t}*( \cos(t)+\cos(6t) )$ using Fourier transform
- Find all $x \in\mathbb R^4$ that are mapped into the zero vector by the transformation $x \mapsto Ax$
- Linear transformation $f (ax+by)=$?
- Is a conformal transformation also a general coordinate transformation?
- Infinite dimensional analysis
Related Questions in REFLECTION
- Reflection matrix in $\Bbb R^2$ (matrix $R$ satisfying $R^2 = 1$)
- A theorem regarding a composition of two reflections
- Reflect a ray off a circle so it hits another point
- What is the equation of a reflected Bézier curve?
- Problems computing the Householder transformation
- Sphere reflection property (geometric proof).
- proof given for spheres to be done for manifolds
- Matrix for the reflection over the null space of a matrix
- How do I calculate the slope of a line knowing one intersection point and the intersection point of that line after two reflection angles?
- Reflection axes on Poincaré half-plane model
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hint: Find the projection $\vec{p}$ of $\vec{u}=\langle1,1,1\rangle$ on $\vec{w}=\langle 2,1,2\rangle$, and then use that the reflection $\vec{r}$ satisfies $\vec{r}+\vec{u}=2\vec{p}$.