The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)
This is the vector equation; getting the parametric form is just a matter of delineating
<em>x</em>(<em>t</em>) = 1 + <em>t</em>
<em>y</em>(<em>t</em>) = 3<em>t</em>
<em>z</em>(<em>t</em>) = 6 + <em>t</em>
Answer:
transpiration and evaporation
Answer:
wait what is your math problem?
Step-by-step explanation:
Answer:
a. In the same vertical line and segment lenght is 12 units.
b. Those are not in the same horizontal or vertical line.
c. In the same vertical line and segment lenght is 7 units.
d. In the same horizontal line and the segment lenght is 9 units.
Step-by-step explanation:
A. the end points are (0,-2) and (0,9). If we represent this two end points on a coordinate axis we can see that these points are in the same vertical line according to the <em>y</em> axis. And the lenght of the segment that joints the pair of points is 12 units lenght.
B. For subsection b the two given end points if we represent those on a coordinate axis we can say that thse two points are not in the same horizntal or verticall line each other. Because non of the numbers of each point match each other in the same axis.
C. The end points given are (3,-8) and (3,-1), and these points represented on a coordinate axis we can say that those are in the same vertical line. And the lenght of the segment each other is 7 units lenght.
D. The end points of subsection D are (-4,-4) and (5,-4) those points represented on a coordinate axis we can see that those are in the same horizontal line and the length of the segment is equal to 9 units.
Answer:
108 inches square.
Step-by-step explanation:
Here
base= b= 4 inches
height = h=w= 3.5 inches
and length = l= 9 inches
The surface area is the total area of all the sides of the prism. So the area of the 2 triangles is given by
Area of the 2 Δs= b* h= 4*3.5= 13.5 inches square
Area of the 3 rectangles = l*w(3)= 3( 9*3.5)= 94.5 inches square.
Total area = 13.5 + 94.5 = 108 inches square
This can be found by applying another formula.
Surface area of the triangular prism = bh + ( s1+s2+s3) H
= 4*3.5 + (9+9+9)3.5
= 13.5 + 94.5= 108 inches square.
where H is the width of the recatngles which is equal to the height of the triangles.
