A plane passing through point (1,0, - 1) and parallel to vectors a = (2,1,1) and B = (1, - 1,0), try to find the plane equation | Math enthusiast | Mathematical art

A plane passing through point (1,0, - 1) and parallel to vectors a = (2,1,1) and B = (1, - 1,0), try to find the plane equation

Let n = (x, y, z) be perpendicular to the vector ab. then n is equal to the cross product of ab

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1. If a plane passes through a point (1,0,1) and is parallel to the vectors a = {2,1,1} and B = {1, - 1,0}, the plane equation is solved?
2. Given that the plane passes through point m (1, - 1,1) n (0,1, - 3) and is parallel to vector a (1,1,1), the plane equation is solved
3. Given the plane intercept equation x / A + Y / B + Z / C = 1, how to get the normal vector of the plane directly through the equation without converting it into a general equation
4. [kneeling] given the normal vector of a plane and the two points it passes through, how to find the equation of the plane? Of course, it's a point method. In fact, you only need to know the point But my question is, if we bring in another known point, the result of the plane equation will be different. Isn't that contradictory?
5. Given that point m (1,2, - 1) is in plane a and a normal vector of plane a is (- 1,1,3), the equation of plane a is obtained
6. In higher mathematics, how to find the normal vector of a plane equation?
7. What does the direction cosine of the normal vector of a plane equation mean?
8. Plane equation defined by normal vector and constant of plane The plane equation defined by normal vector N and constant D is x · n = D
9. If the intersection of the image of the first-order function y = KX + B and the inverse scale function y = KX is (2,3), then K=______ ，b=______ ．
10. XY + 2 = K + 8. When k is constant, X is proportional to y?
11. Given the parallel vector of a plane and two points passing through the plane, how to solve the plane equation
12. In the geometric sense of vector, it is the distance (i.e. length) from the point of the vector on the coordinate plane to the origin / / must be to the origin (0,0)? Must go to the origin (0,0)? From point (4,5) to point (2,2), no?
13. It is known that I is an imaginary unit. In the complex plane, Z1 = 1 + I, Z2 = 2 + 3I correspond to points a and B, O is the origin, and vectors OP, OA and ob satisfy OP = OA + xob, If point P is in the fourth image term Then the value range of X is?
14. Points a and B (5,0) satisfy the vector OA * vector ob = vector OA * vector Ba, │ vector OA + vector ob = √ 185, and then calculate the a coordinate
15. Given vector | OA | = 1, | ob | = √ 3, OA * ob = 0, point C is on line ab Given vector | OA | = 1, vector | ob | = √ 3, vector OA * vector ob = 0, point C is on line AB, and angle AOC = 30 °, find (1) vector OA * vector OC (2) let vector OC = MOA + nob, find the value of real numbers m and n
16. Let | vector OA | = | vector ob | = 3, ∠ AOB = 60 °, then | vector OA + vector ob|= By the way!
17. What does OA vector multiply ob vector = 0 mean
18. Known vectors OA = (1,3), OB = (2,5) Given the vector OA = (1,3), OB = (2,5), OC = (m, m), if AB is perpendicular to BC, what is the real number m
19. If the vector OA = (3,2) ob = (4,7), then AB =?
20. AO*BO=AB?