Which equation is equivalent to -7x+11=32

Find the distance from the point to the line. (-1,-2,1);x=4+4t, y=3+t, z=6-t .The distance is ____ Typn exact answer, using radi

lawyer [7]

Answer:

The distance is<u> 4.726 </u>

Step-by-step explanation:

we need to find the distance from the point to the line

Given:- point (-1,-2,1) and line ; x=4+4t, y=3+t, z=6-t .

used formula $d=\frac{|a\times b|}{|a|}$

Let point P be (-1,-2,1)

using value t=0 and t=1

The point Q (4 , 3, 6) and R ( 8, 4, 5)

Let a be the vector from Q to R : a = < 8 - 4, 4 - 3, 5 - 6 > = < 4, 1, -1 >

Let b be the vector from Q to P: b = < -1 - 4, -2 - 3, 1 - 6> = < -5, -5, -5 >

The cross product of a and b is:

$a \times b= \begin{vmatrix} i & j & k\\ 4 &1&-1\\-5 &-5&-5\\ \end{vmatrix}$

= -6i+15j-15k

The distance is : $d=\frac{\sqrt{(-6)^{2}+(15)^{2}+(-15)^{2}}}{\sqrt{(4)^{2}+(1)^{2}+(-1)^{2}}}$

$=\frac{\sqrt{36+225+225}}{\sqrt{16+1+1}}$

$d=\frac{\sqrt{486}}{\sqrt{18}}$

≈4.726

Therefore, the distance is<u> 4.726 </u>

3 0

3 years ago

I need help. Find the values of a b and c. Note diagram (attached) is not to scale.

shusha [124]

Please read the attached file

7 0

4 years ago

PLEASE HELP ASAP!!

kolezko [41]

Is it a rotation 90° a clockwise about the origin?

6 0

3 years ago

Read 2 more answers

The gas tank of Dave car has a capacity of 12 gallons. The tank was 3/8 full before Dave filled it to capacity. It cost him $2.5

forsale [732]

Answer: $18.75

Step-by-step explanation:

1 - 3/8 = 5/8

12 x 5/8 = 7.5

7.5 x 2.5 = 18.75

8 0

2 years ago

1. A shipping company charged $15 to ship a package and 5% of the shipping charge for insurance on the package. What was the tot

astra-53 [7]

Just simply multiply and then add'

15*.05= .75 so .75 was added to the price

now add

.75+15= 15.75

So the answer is $15.75

8 0

4 years ago

Read 2 more answers

Which equation is equivalent to -7x+11=32​

Which equation is equivalent to -7x+11=32