I need problem 1 please with all work shown

\ Given the two vectors in standard position

vec(A)=(:10,1:)

and

vec(B)=(:13,-7:)

,\ Show the projection

Proj_(vec(B))vec(A)

by following the steps listed:\ (a) Graph the vectors on the grid provided, use a straight edge to make them neat.\ (b) Draw a dashed line on top of vector

vec(B)

, but running "infinitely" in both directions.\ This will be the line to project onto.\ (c) Calculate the projection vector using the formula, use this to determine where the altitude from

vec(A)

\ will intersect the line containing

vec(B)

.\ (d) Draw the perpendicular altitude from vector

vec(A)

onto the line containing

vec(B)

, noting the right angle.\ (e) Graph the projection vector from the origin point, ending at the point of the altitude's intersection\ with the dashed line containing

vec(B)

.\ Using these two vectors, follow the same directions as the last question:\

vec(P)=

the vector from the point

(-2,1)

to the point

(0,8)

\

vec(V)=

the vector from the point

(-2,1)

to the point

(-8,0)

\ Calculate and show the projection

Proj_(vec(V))vec(P)

.\ Graph the vectors

vec(C)=8hat(i)-hat(j),vec(D)=5hat(i)-5hat(j)

\ Then find and graph the components of

vec(D):,vec(W)_(1),vec(W)_(2)

such that

vec(W)_(1)=Proj_(vec(C))vec(D)

, and

vec(W)_(1)+vec(W)_(2)=vec(D)

\ Also show by calculation that

vec(W)_(1)_(|)_(v)ec(W)_(2)

\ Calculate the force,

F

lbs, required to keep an object weighing

700lbs

from sliding down a ramp inclined\ by

37\\\\deg

from the horizontal. Draw a sketch showing the incline, object and the vectors used on the object.\ Melinda is pushing a chair along a 5 meter straight path through her living room. She is standing, pushing\ at the top of the chair with a force of 30 newtons at a

22\\\\deg

angle of depression from the horizontal.\ (a) Calculate the work done in moving the chair.\ (b) How could Melinda re-arrange herself to make the energy use more efficient?

Solve the following problems, and show all your work: 1. Given the two vectors in standard position A=10,1 and B=13,7, Show the projection ProjBA by following the steps listed: (a) Graph the vectors on the grid provided, use a straight edge to make them neat. (b) Draw a dashed line on top of vector B, but running "infinitely" in both directions. This will be the line to project onto. (c) Calculate the projection vector using the formula, use this to determine where the altitude from A will intersect the line containing B. (d) Draw the perpendicular altitude from vector A onto the line containing B, noting the right angle. (e) Graph the projection vector from the origin point, ending at the point of the altitude's intersection with the dashed line containing B. 2. Using these two vectors, follow the same directions as the last question: P= the vector from the point (2,1) to the point (0,8) V= the vector from the point (2,1) to the point (8,0) Calculate and show the projection ProjVP. 3. Graph the vectors C=8i^j^,D=5i^5j^ Then find and graph the components of D:W1,W2 such that W1=ProjCD, and W1+W2=D Also show by calculation that W1W2 4. Calculate the force, F lbs, required to keep an object weighing 700lbs from sliding down a ramp inclined by 37 from the horizontal. Draw a sketch showing the incline, object and the vectors used on the object. 5. Melinda is pushing a chair along a 5 meter straight path through her living room. She is standing, pushing at the top of the chair with a force of 30 newtons at a 22 angle of depression from the horizontal. (a) Calculate the work done in moving the chair. (b) How could Melinda re-arrange herself to make the energy use more efficient