Vector has x and y components of -8.80 cm and 18.0 cm, respectively; vector has x and y components of 12.2 cm and -6.80 cm, respectively. If - + 3 = 0, what are the components of ? x = cm y = cm

Question:

Vector A has x and y components of −8.80 cm  and 18.0 cm , respectively; vector B has x and  y components of 12.2 cm and −6.80 cm , respectively.  If A − B +3 C = 0, what are the components of C?

x = ___ cm

y = ___ cm

x = 7.0cm

y = -8.27cm

Step-by-step explanation:

For a vector F, with x and y components of a and b respectively, its unit vector representation is as follows;

F = ai + bj              [Where i and j are unit vectors in the x and y directions respectively]

Using this analogy, let's represent vectors A and B from the question in their unit vector notation.

A has an x-component of -8.80cm and y-component of 18.0cm

B has an x-component of 12.2cm and y-component of -6.80cm,

In unit vector notation, these become;

A = -8.80i + 18.0j

B = 12.2 i + (-6.80)j = 12.2i - 6.80j

Also, there is a third vector C. Let the x and y components of C be a and b respectively. Therefore,

C = ai + bj

Now,

A - B + 3C = 0                [substitute the vectors]

=> [-8.80i + 18.0j] - [12.2 i -6.80j] + [3(ai + bj)] =  0        [open brackets]

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3(ai + bj) =  0

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj =  0

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj =  0  [collect like terms and solve]

=> -8.80i  - 12.2 i  + 3ai + 6.80j + 18.0j + 3bj =  0

=> -21.0 i  + 3ai + 24.8j + 3bj =  0       [re-arrange]

=> 3ai + 3bj = 21.0i - 24.8j

Comparing both sides shows that;

3a = 21.0  (i)

3b = -24.8    (ii)

From equation (i)

3a = 21.0

a = 21.0 / 3 = 7.0

From equation (ii)

3b = -24.8

b = -24.8 / 3

b = -8.27

Therefore, the x-component and y-component of vector B which are a and b, are 7.0cm and -8.27cm respectively.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|