Which of these points is the closest to the point (7, 1) ?

Step-by-step explanation:

Solution

The general equation of the plane passing through (2,5,−3) is

a(x−2)+b(y−5)+c(z+3)=0 (1)

Now, this plane passes through B(−2,−3,5) and C(5,3,−3).Then we have

a(−2−2)+b(−3−5)+c(5+3)=0

⇒−4a−8b+8c=0

⇒−a−2b+2c=0 (2)

a(5−2)+b(3−5)+c(−3+3)=0

⇒3a−2b=0 (3)

Solving (2) and (3) we get

0+4

a

=

6−0

b

=

2+6

c

⇒

4

a

=

6

b

=

8

c

=λ(say)

⇒a=4λ,b=6λ,c=8λ

Substituting the values of a,b and c in (1), we get

4λ(x−2)+6λ(y−5)+8λ(z+3)=0

⇒4(x−2)+6(y−5)+8(z+3)=0

⇒4x+6y+8z−14=0

⇒2x+3y+4z−7=0

This is the equation of the plane determined by the points A(2,5,−3),B(−2,−3,5) and C(5,3,−3)

Now, the distance of this plane from the point (7,2,4) is

D=

2

2

+3

2

+4

2

∣(2×7+3×2+4×4)−7∣

=

4+9+16

∣(14+6+16)−7∣

=

4+9+16

∣36−7∣

=

29

29

=

29

29

×

29

29

=

29

units.

Thus, the distance between the point (7,2,4) and the plane 2x+3y+4z−7=0 is

29

units.

were is the equation

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|