Unit vector Definition and 167 Threads

Hello everyone, new to the forums but I have used the information here for help in the past. Having trouble with a specific part of a problem.1. A 0.65 kg block of ice is sliding by you on a very slippery floor at 2.5 m/s. As it goes by, you give it a kick perpendicular to its path. Your foot...

Homework Statement Vector a1 + vector a2 = 5*vector a3 Vector a1 - vector a2 = 3*vector a3 Vector a3 = 2i + 2j (i and j are the vector components) Express 1) vector a1 and 2) vector a2 in unit vector notation Homework Equations Vector R = Ax + Yx The Attempt at a Solution I took the first...

Homework Statement Vector a1 + vector a2 = 5*vector a3 Vector a1 - vector 12 = 3*vector a3 Vector a3 = 2i + 2j (i and j are the vector components) Express 1) vector a1 and 2) vector a2 in unit vector notation Homework Equations Vector R = Ax + Yx The Attempt at a Solution I...

1. Is v-hat a unit vector or a vector? If it is a unit vector how do you symbolically represent a vector? If it is a vector how do you symbolically represent a unit vector? 2. Is v-hat the same thing as v with an arrow over it?

Find the expression for the unit vector tangential to the curve given in spherical coordinates by r = 1, \phi = 2\theta, 0 \leq \theta \leq \pi the equation for the differential length vector for spherical coordinates: dl = drar + rd\thetaa\theta + rsin(\theta)d\phia\phi where ar, a\theta, and...

Homework Statement Given the two vectors written in component-unit vector form below: D = 3\hat{i} - \hat{j} E = 2\hat{i} + 4\hat{j} a.) Find the unit vector in the same direction as D b.) Find the cross product of D x E c.) Write the vector D in magnitude direction form Homework...

Homework Statement there are two vectors a and b a=3i+2j+k b=2i+j+2k Find the unit vector perpendicular to a and b Homework Equations | A|^a=A The Attempt at a Solution I don't kno how to start

Homework Statement Show that if the vector \textbf{v}_1 is a unit vector (presumably in \Re^n) then we can find an orthogonal matrix \textit{A} that has as its first column the vector \textbf{v}_1. The Attempt at a Solution This seems to be trivially easy. Suppose we have a basis \beta for...

I'll be greatful for any hint. Imagine you walk over the contourlines of the map of a mountain (really! that's the question) with a gradient of h(x,y)=2xy, x^2). You are at point (1,3) and you want to walk downslope at an angle of 45 degrees. calculate the unit vector in order to find out in...

Hey. Here is the question: \underline{b}= -8\underline{i} - 6\underline{j} I need to find a unit vector perpendicular to vector b. Ive come up with the following: 10 \times |\underline{x}| \cos 90 = \underline{b} \bullet \underline{x} I don't know if what I've done is even...

I'm currently taking my first physics class, and on the very first day, my teacher began discussing vectors as if everyone knew what Unit Vectors were. I've managed to understand most of his lecture thus far, but I still don't understand- How do you convert from Unit vectors (denoted by i...

at point T(2,3,-4) in rectangular coordinate system, how would I express the Z unit vector in the spherical system and the R unit vector in the rectangular system? I know T in spherical coordinates is (5.385,-42 degrees,56.3 degrees) but i have no idea how i would express a unit vector in a...

I have a unit vector frac{{{\rm - 2}}}{{\sqrt {{\rm 89}} }},\frac{{\rm 7}}{{\sqrt {{\rm 89}} }},\frac{{{\rm - 6}}}{{\sqrt {{\rm 89}} }} I need to figure out a vector with a length of 4 with that as a unit vector. Now I'm thinking that I can just do… t(\frac{{{\rm - 2}}}{{\sqrt {{\rm 89}}...

Please help. Given the 3 vectors a = -21 + 3j - k, b = 41 - j + 2k and c = -3i + 2j - 3k: 1. Find the unit vector perpendicular to a and b + c. 2. Evaluate a . b x c I'm completely clueless on how to approach the first question. Any help would be great. I'm not sure which product...

How do you find a unit vector normal to the surface of scalar field \phi(x,y,z)=x^2y+3xyz+5yz^2? Should you apply the \nabla operator to it?

Hi, I'm wondering if anyone knows how to input a unit vector that lies between X and Y axes, into a Master Physics answering box. One of the questions I'm working on required a unit vector (to point a direction) to be part of the answer. I know that the direction is between the X and Y...

In Figure 13-34, a square of edge length 21.0 cm is formed by four spheres of masses m1 = 6.00 g, m2 = 3.00 g, m3 = 1.00 g, and m4 = 6.00 g. In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.40 g? Well by using Newton's Law of...