iarc6io
2022-07-27
Answered

Find the unit vector along the line joining point (2, 4, 4) to point (-3,2,2).

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Marshall Mcpherson

Answered 2022-07-28
Author has **11** answers

Vector from point 1 to point 2 is given by:

(-3-2,2-4,2-4) = (-5,-2,-2)

$length=\sqrt{{5}^{2}+{2}^{2}+{2}^{2}}=\sqrt{33}$

So unit vector is:

$(-5/\sqrt{33},-2/\sqrt{33},-2/\sqrt{33})$

(-3-2,2-4,2-4) = (-5,-2,-2)

$length=\sqrt{{5}^{2}+{2}^{2}+{2}^{2}}=\sqrt{33}$

So unit vector is:

$(-5/\sqrt{33},-2/\sqrt{33},-2/\sqrt{33})$

asked 2021-05-14

Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR

Consider the points below

P(1,0,1) , Q(-2,1,4) , R(7,2,7)

a) Find a nonzero vector orthogonal to the plane through the points P,Q and R

b) Find the area of the triangle PQR

Consider the points below

P(1,0,1) , Q(-2,1,4) , R(7,2,7)

a) Find a nonzero vector orthogonal to the plane through the points P,Q and R

b) Find the area of the triangle PQR

asked 2021-06-01

Find the vectors T, N, and B at the given point.

$r(t)=<{t}^{2},\frac{2}{3}{t}^{3},t>$ and point $<4,-\frac{16}{3},-2>$

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Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at

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- A⃗ = (4, 3) , B⃗= (2, 5)

asked 2021-01-28

Given the vector

Vector T is the unit tangent vector, so the derivative r(t) is needed.

Vector N is the normal unit vector, and the equation for it uses the derivative of T(t).

The B vector is the binormal vector, which is a crossproduct of T and N.

asked 2022-06-12

Finding the transformation matrix given the transformation

Given the Transformation $P({x}_{1},{x}_{2},{x}_{3})=({x}_{2},{x}_{3})$, and I'm supposed to find the transformation matrix $A$ so that $A({x}_{1},{x}_{2},{x}_{3})=({x}_{2},{x}_{3})$

How do I do this? I managed to find it for a previous question through trial and error but it took me a while and I need a good mathematical way to do it

Given the Transformation $P({x}_{1},{x}_{2},{x}_{3})=({x}_{2},{x}_{3})$, and I'm supposed to find the transformation matrix $A$ so that $A({x}_{1},{x}_{2},{x}_{3})=({x}_{2},{x}_{3})$

How do I do this? I managed to find it for a previous question through trial and error but it took me a while and I need a good mathematical way to do it