Answer:
The equation of plane is x-y+z=12.
Step-by-step explanation:
It is given that the plane passing through the point (0,0,6) perpendicular to x=1-t y=2+t z=4-2t.
The given line is perpendicular to required plane, so coefficients of t represents the normal vector.
Normal vector is
If a plane passes through and having normal vector
, then the equation of plane is
Multiply both sides by -1.
Therefore, the equation of plane is x-y+z=12.
Answer:
The common difference d in the given sequence is -17
Step-by-step explanation:
We need to find the common difference d of the following sequence 9 -8 -25 -42 -59
We have a₁ = 9
and a₂ = -8
The formula used is:
By putting values we can find the value of d
We have n=2, a₂ = -8, a₁ = 9 and we need to find d
So, the common difference d in the given sequence is -17
Answer:
Step-by-step explanation:
The given point is (-2, 3), labeled point A in the attachment.
As you know, the distance from the x-axis is given by the y-coordinate. Here, that distance is ...
3 units from the x-axis
__
The distance from the y-axis is given by the magnitude of the x-coordinate. Here, that distance is ...
2 units from the y-axis
Note that the negative coordinate value means the point is located that distance to the left of the y-axis.
__
Reflecting the point across the y-axis means choosing a point that is the same distance (2 units) right of the axis instead of left of the axis. The sign of the x-coordinate value will be positive, instead of negative. (The y-coordinate remains unchanged,)
__
The reflected point is (2, 3).
_____
<em>Additional comment</em>
As we have seen, reflection across the y-axis changes the sign of the x-coordinate:
(x, y) ⇒ (-x, y) . . . . reflection across the y-axis
Similarly, reflection across the x-axis changes the sigh of the y-coordinate:
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
