Given that a (1, - 2,9), B (10, - 1,6) and C (2,4,3) constitute a surface, find the value of D (5,0.5,) Z on the surface, and tell me the formula and source

Given that a (1, - 2,9), B (10, - 1,6) and C (2,4,3) constitute a surface, find the value of D (5,0.5,) Z on the surface, and tell me the formula and source

Thinking:
Vector AB = (9,1, - 3)
Vector AC = (1,6, - 6)
AB, AC are not collinear
So any vector in the plane of points a, B and C can be represented by vectors AB and AC
Vector ad = (4,2.5, Z-9) = m · vector AB + n · vector AC = (9m + N, M + 6N, - 3m-6n)
A system of linear equations with three variables can be obtained
9m+n=4
m+6n=2.5
-3m-6n=z-9
From the first two formulas, M = 43 / 106, n = 37 / 106
Substituting into the third formula, z = 603 / 106
I don't know if it's wrong. It's such an embarrassing number
The method comes from the following ideas
Basic theorem of plane vector
If E1 and E2 are two non collinear vectors in the same plane, then any vector a in the plane can be expressed as a = λ 1E1 + λ 2e2, where the number pair (λ 1, λ 2) is unique
In this question, I use M and N to represent number pairs (because 1 and 2 in λ 1 and λ 2 are not easy to be subscript in Baidu)

The distance between a and B measured on a map of 1:3000000 scale is 15cm, if drawn on a map of 1 / 100000 scale
How many centimeters should be drawn between a and B?

15*3000000/100000=450cm

Given the function f (x) = 2cos (2x - π 4), X ∈ R. (1) find the minimum positive period and monotone increasing interval of function f (x); (2) find the minimum and maximum value of function f (x) in the interval [- π 8, π 2], and find the value of X when the maximum value is obtained

Solution (1) because f (x) = 2cos (2x - π 4), the minimum positive period of function f (x) is t = 2 π 2 = π. From the monotone interval - π + 2K π ≤ 2x - π 4 ≤ & nbsp; 2K π, we get - 3 π 8 + K π ≤ x ≤ π 8 + & nbsp; K π, so the monotone increasing interval of function f (x) is [- 3 π 8 + K π & nbsp;, & nbsp; π 8 + & nbsp; K π] K is a positive integer. (2) because f (x) = 2cos (2x - π 4) is in the interval [& nbsp; -π 8, π 8] is an increasing interval, and in the interval [π 8, π 2] is a decreasing function, and f (& nbsp; - π 8) = 0f (π 8) = 2, f (π 2) = - 1, so the maximum value of function f (x) in the interval [- π 8, π 2] is 2, then x = π 8: the minimum value is - 1, then x = π 2

A and B are two numbers. A is 10. B is one third of a and B. then the two numbers are equal. How much is B equal? How much is B equal

Let B be X
Then 2 / 3 * x = 10 + 1 / 3 * x;
So x = 30

Senior high school mathematics compulsory five inequalities
Function f (x) = MX & # 178; - MX + 6 + M
(1) If f (x) < 0 holds for m ∈ [- 2,2], find the value range of X
(2) If f (x) < 0 holds for X ∈ [1,3], the range of M is obtained

(1) There are three cases, - 2 ≤ M

A and B two cars leave from AB two cities at the same time. A's speed is three fifths of B's. The two cars meet 24 kilometers from the midpoint. How many kilometers is the distance between AB and a?
I figured out 60 kilometers

Primary school mathematics problems, do not set so unknowns
The speed of a is three fifths of that of B, and the driving distance in the same time is three fifths of that of B,
When they meet, a and B walk the distance of AB together, but a only walk 3 / 5 of B's distance. Therefore, at the meeting point, the proportion of a's distance to ab's distance is (3 / 5) / (3 / 5 + 1) = 3 / 8, and B's distance is 5 / 8. That is to say, the meeting point is at the position of 3 / 8,
Therefore, the total length of AB is 24 / (1 / 2-3 / 8) = 192 km

Solving inequality 1. (x ^ 2-4x + 3) (3 + 2x-x ^ 2)

1.（x-1)(x-3)*-(x-3)(x+1)0
X not = 3, x > 1 or X

The two passenger and freight cars leave each other from a and B. when they meet, the distance is 5:4. After the meeting, the freight car travels 18 kilometers more per hour than before. The passenger car moves forward at the original speed and ends at the end of the day
When the two vehicles arrive at the other party's departure station at the same time, how many kilometers is the distance between the two places?
Please use arithmetic to answer, thank you very much!

If according to the original speed, when the bus arrives, the truck 4 / 5 = 0.84 * 0.8 = 3.25-3.2 = 1.81.8 / (5 + 4) = 0.2 = 1 / 5, the distance between the truck and the starting point of the bus and 1 / 5 of the whole journey, (5 / 9-1 / 5) = 16 / 451 / 5:16 / 45 = 9:1618 / (9 / (9 + 16)) = 5050-18 = 3232 * (5 / 4) = 4040 * 10 = 4

If the non-zero vector a, B satisfies | a | = | B |, (2a + b) B = 0, find the angle between a and B,

Let the included angle be a, then AB = | a | B | cosa = | B | & sup2; cosa
(2a+b)b=2ab+b²=2|b|²cosA+|b|²=0
∵|b|≠0
∴2cosA+1=0
That is, cosa = - 1 / 2
That is, a = 120 degree

There are two teams a and B, team a is twice as big as team B. team a has nine people and team B has eight people. The number of team a is half of team B. how many people are there in team a?

Suppose there are x people in team B, then there are 2x people in team A. The equation 2 (2x-9) = X-8 is obtained. But the number calculated in this way is not an integer. Maybe there is something wrong with the number you gave. The algorithm must be correct. Check the number