For $\|3v\| = 1$, I isolated $v$ and got: $\|v\| = 1/3$.
I used $\|u+v\|^2 = (u+v)\cdot(u+v)$ and got to
$$\|u+v\|^2 = \|u\|^2 + 2(u \cdot v) + \|v\|^2$$
$$(1) = (1) + 2(u \cdot v) + (1/9)$$
$$u \cdot v = -1/18$$
Is my answer/process correct?
2026-04-13 02:52:58.1776048778
Suppose $\|u\|=1=\|3v\|$ . If $\|u+v\|=1$ then $u \cdot v=?$
87 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 SOLUTION-VERIFICATION
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Exercise 7.19 from Papa Rudin: Gathering solutions
- Proof verification: $\forall n \in \mathbb{Z}, 4\nmid(n^2+2)$
- Proof verification: a function with finitely many points of discontinuity is Riemann integrable
- Do Monoid Homomorphisms preserve the identity?
- Cantor-Lebesgue's theorem
- If $a$ is an integer, prove that $\gcd(14a + 3, 21a + 4) = 1$.
- Number theory gcd
- $|G| > 1$ and not prime implies existence of a subgroup other than two trivial subgroups
- Prove/Disprove: Sum of im/ker of linear transformation contained in ker/im of each linear trasnfromation
Related Questions in VECTORS
- Proof that $\left(\vec a \times \vec b \right) \times \vec a = 0$ using index notation.
- Constrain coordinates of a point into a circle
- Why is the derivative of a vector in polar form the cross product?
- Why does AB+BC=AC when adding vectors?
- Prove if the following vectors are orthonormal set
- Stokes theorem integral, normal vector confusion
- Finding a unit vector that gives the maximum directional derivative of a vector field
- Given two non-diagonal points of a square, find the other 2 in closed form
- $dr$ in polar co-ordinates
- How to find reflection of $(a,b)$ along $y=x, y = -x$
Related Questions in INNER-PRODUCTS
- Inner Product Same for all Inputs
- How does one define an inner product on the space $V=\mathbb{Q}_p^n$?
- Inner Product Uniqueness
- Is the natural norm on the exterior algebra submultiplicative?
- Norm_1 and dot product
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
- Orthonormal set and linear independence
- Inner product space and orthogonal complement
- Which Matrix is an Inner Product
- Proof Verification: $\left\|v-\frac{v}{\|v\|}\right\|= \min\{\|v-u\|:u\in S\}$
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?