121 Answered Questions for the topic vector

#### Find a basis of the subspace R4 consisting of all vectors

Find a basis of the subspace of R4 consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2]

Vector Coordinate

11/25/14

#### Find the coordinate vector of x with respect to the basis B

Find the coordinate vector of x=[-1,2,4] with respect to the basis B={[1,4,6],[0,1,-4],[0,0,1]}
|x|B=

#### Express the vector v as a linear combination of x and y

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1].
v=?x+?y

#### express the vector v as a linear combination

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1]
v=?x+?y

#### Find a vector v in R3 such that H=span(v)

Let H be the set of all vector of the form [-4s,-3s,5s]. Find a vector v in R3 such that H=span {v}
v=?

#### Express the vector v as a linear combination of x and y

Express the vector v= [6,2] as a linear combination of x= [-4,-1] and y[-5,-1]
v=?x+?y

#### The crossproduct of the dots are

You are looking down at a map. A vector U with |U| 1 points north and a vector V with |V|= 9 points northeast. The crossproduct UxV points:A) south?B) northwest?C) up?D) down ?
The magnitude...
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#### Find a unit vector with positive first co-ordinate

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-5, -5, -4),
Q = (-1, -1, 0), and R = (-1, -1, 5).

#### Find an equation of the plane

Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way

#### Find the dot product of x and y

Let x = [-4, 4,5] and y=[0,0,-3]
Find the dot product of x and y
x.y=?

#### Find the vector w=2u-3v and its additive inverse.

Let u=(1,-1,0) and v=(1,-2,-3). Find the vector w=2u-3v and its additive inverse.
w=
-w=

#### Find the angle between the vectors

Find the angle between the vectors
[1
4
-5]
and
[5
-5
4]

#### Applications of the Dot Product (Vectors)

Determine the angle between vector PQ and the positive x-axis, given endpoints P(4,7) and Q (8,3)

#### Applications of the Dot Product (Vectors)

Determine the interior angles of triangle ABC for A(5,1), B(4, -7), and C (-1,-8)

05/17/14

#### Applications of the Dot Product (Vectors)

A force, F of 25 N is acting in the direction of a = (6,1).
a) Find a unit vector in the direction of a.
b) Find the Cartesian vector representing the force, f, using your answer from part a)
more

Vector

06/07/13

#### Find the unit vector?

Let f(x, y, z)=yz+xz-6. At the point x=1, y=1, z=1, find the unit vector that points in the direction for which f is increasing at the fastest rate.

Vector Math

06/06/13

#### Compute the curl?

Let F(x, y) be the vector field ((x-y)/(x^2+y^2), (x+y)/(x^2+y^2)). Compute curl(F).

Vector

05/18/13

#### Find a potential function for the vector field?

Find a potential function for the vector field f(x, y)=2x/y i+(1-x^2)/y^2 j.

Vector

04/01/13

#### Find the principal unit normal vector?

Find the principal unit normal vector to the curve defined by r(t)=<t, t^2>.
T(t)=1/sqrt(1+4t^2)i+2t/sqrt(1+4t^2)j
I need to find T'(t) using quotient rule but don't know how. Show your steps.
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