Question

Find the projection of **u** = −**i**
+ **j** + **k** onto **v** =
2**i** + **j** − 7**k**.

Answer #1

if any doubt plz comment

u = 2i − j + k
v = 3j − 4k
w = −5i +
7k
Find the volume of the parallel face determined by the
vectors.

2.
a. Given u = (9,7) and v = (2,3), find the projection of u onto
v. (ordered pair)
b. Find the area of the parllelogram that has the given vectors
u = j and v = 2j + k as adjacent sides.

Letu=2i−3j+k,v=i+4j−k,andw=j+k.
(a) Find u × v and v × u, and show that each of those vectors
is orthogonal to both u and v.
(b) Find the area of the parallelogram that has u and v as
adjacent sides.
(c) Use the triple scalar product to find the volume of the
parallelepiped having adjacent
edges u, v, and w.

U= [2,-5,-1] V=[3,2,-3] Find the orthogonal projection of u onto
v. Then write u as the sum of two orthogonal vectors, one in
span{U} and one orthogonal to U

Let a = 2i -3k; b= i+j-k
1) Find a x b.
2) Find the vector projection of a and b.
3) Find the equation of the plane passing through a with normal
b.
4) Find the equation of the line passing through the points a and
b.
Please help and show your steps. Thank you in
advance.

Consider the parallelepiped with adjacent edges
u=6i+3j+k
v=i+j+6k
w=i+5j+4k
Find the volume.
V=

Find the fundamental vector product.
1. r(u, v) = (u 2 − v 2 ) i + (u 2 + v 2 ) j + 2uv k.
2. r(u, v) = u cos v i + u sin v j + k.

Find the orthogonal projection of u onto the
subspace of R4 spanned by the vectors
v1, v2 and
v3.
u = (3, 4, 2, 4) ;
v1 = (3, 2, 3, 0),
v2 = (-8, 3, 6, 3),
v3 = (6, 3, -8, 3)
Let (x, y, z, w) denote the
orthogonal projection of u onto the given
subspace. Then, the components of the target orthogonal projection
are

Find an equation of the tangent plane to the parametric surface
r=(u,v)=ucosv I +usinv j +vk at u=1, v=pi/3
Find the surface area of the parametric surface r(u,v)=5sinucosv
I + 5sinusinv j+ 5cosu k, for 0 ,<= u <=pi and o<=v<=
2pi

Find the position vector of a particle that has acceleration
2i+4tj+3t^2k, initial velocity v(0)=j+k and initial position
r(0)=j+k

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