QUESTION 1 Determine the work done by the force
F=31+] + k in moving an object through
displacement T = 7 -7 -K​

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is

W = F • r cos(θ)

The cosine of the angle between the vectors can be obtained from the dot product identity,

a • b = ||a|| ||b|| cos(θ)   ==>   cos(θ) = (a • b) / (||a|| ||b||)

so that

W = (F • r)² / (||F|| ||r||)

For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is

W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   W ≈ 5.12 J

(assuming F and r are measured in Newtons (N) and meters (m), respectively).

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

the domain of a function is the set of input values, x , for which a function is defined. the domain is shown in the left oval in the picture below. the function provides an output value, f(x) , for each member of the domain.