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Solve the plane equation of the straight line x + 3 / 3 = y + 2 / - 2 = Z / 1 and X + 3 / 3 = y + 4 / - 2 = Z + 1 / 1
The normal vectors of two lines are N1 = (3, - 2,1), N2 = (3, - 2,1), so L1 / / L2, the line L1 passes through point a (- 3, - 2,0), the line L2 passes through point B (- 3, - 4, - 1), so the vector AB = (0, - 2, - 1), so the normal vector of the plane passing through line L1 and L2 is N1 × AB = (4,3, - 6)
The plane equation which passes through the point P (- 1,2, - 3) and is perpendicular to the straight line x = 3 + T, y = t, z = 1-T is solved
The straight line x = 3 + T, y = t, z = 1-T is written as a symmetric expression x-3 = y = (Z-1) / - 1, so the direction vector of the straight line (1,1, - 1)
If the line x = 3 + T, y = t, z = 1-T is perpendicular to the plane equation, then the normal vector of the plane and the direction vector of the line (1,1, - 1)
So we use the direction vector (1,1, - 1) of the straight line as the normal vector of the plane
The point method obtains the plane equation x + 1 + y-2-z-3 = 0, x + y-z-5 = 0
Solve the plane equation of point P (- 1,2, - 3) and perpendicular to the line x = 3 = + T, y = t, z = 1-t
This x = 3 = + T should be 3 + t
Let the coordinates of the intersection of the plane and the line be q = (x, y, z), then obviously, the coordinates still satisfy the parameter equation of the line, that is, the coordinates can be written as q = (3 + T, t, 1-T)
Now we know that the straight line determined by P and Q is perpendicular to the known straight line. According to the condition of perpendicularity, we can list an equation, solve t, and then the plane equation will come out
The plane equation which passes through the point P (1, - 3,2) and is perpendicular to the line L: (x-3) / 1 = (y + 7) / 2 = Z / 3 is solved
The normal vector of a plane is the direction vector of a straight line. So the point method equation of a plane is: (x-1) + 2 (y + 3) + 3 (Z-2) = 0. That is: x + 2Y + 3z-1 = 0
RELATED INFORMATIONS
- 1. If a line passes through point m (a, 3) and point n (1, 2), the equation of the line is solved
- 2. The equation of a straight line passing through a point (1,0-2), parallel to the plane 3x + 4y-z + 6 = 0 and perpendicular to the straight line (x-3) / 1 = (y + 2) / 4 = Z / 1 is obtained
- 3. Solve the plane equation which passes through the point m (3,1, - 2) and the straight line la-4 / 5 = B + 3 / 2 = C / 1
- 4. For example, there are two points a (1,0) and B (- 1,0) on the plane of the graph, and the known equation of the circle is (x-3) ^ 2 + (y-4) ^ 2 = 2 ^ 2 Find the maximum area of ABP1 with a point p1 on the circle and find out the area
- 5. There are two points a (- 1,0) and B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find ap2 There are two points a (- 1,0), B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find the coordinates of point P when ap2 + bp2 takes the minimum value The equation of a circle is that the square of (x-3) plus the square of (y-4) equals 4 [2 is the square] What we need is also the square of AP plus the square of BP
- 6. Mathematical problems of plane rectangular coordinate system under seven "Monster eats peas" is a computer game. The symbols in the picture indicate the locations where the "monster" passes successively. If (1,2) is used to indicate the third location where the "monster" passes according to the route indicated by the arrow in the picture, can you show the other locations where the "monster" passes in the same way?
- 7. 1995-1+2-3+4-5+… +1948-1949=______ ．
- 8. 1995-1+2-3+4-5+… +1948-1949=______ ．
- 9. 1 2 3 4 5 =200 Adding addition, subtraction, multiplication and division to the left side of the equation can sum two numbers into one number, or add brackets, but the order cannot be changed to make the equation hold Example (1 + 23) * 4-5 = 91, but it is not equal to 200
- 10. The vertex of the parabola is at the origin of the coordinate, and the focus coincides with a focus of hyperbola Y / 5-x / 4 = 1
- 11. Given that the line segment AB = a, P is a point on AB, and AP = ((radical 5-1) / 2) * a, find the ratio of AP to Pb, AB to AP, and ask whether the four line segments AP, Pb, AB and AP are equal
- 12. Given that point P is a point on line AB, the length ratio of AP to Pb is 2:3. If AP = 4cm, find the length of Pb and ab
- 13. Let the moving line l be perpendicular to the x-axis and intersect with the ellipse x2 + 2Y2 = 4 at two points a and B. P is the moving point on L which satisfies the vector PA multiplied by the vector Pb = 1. The trajectory equation of point P is obtained
- 14. Ellipse X & # 178 / 9 + Y & # 178 / 5 = 1, the line between a point P on the line x = - 9 / 2 and the left focus f intersects the ellipse at two points a and B respectively, if the vector PA = λ AF, Ellipse X & # 178 / 9 + Y & # 178 / 5 = 1, the line between a point P and the left focus f on the straight line x = - 9 / 2 intersects ellipse at two points a and B respectively. If vector PA = λ, vector AF, vector Pb = μ, vector BF, calculate λ + μ
- 15. Hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) f is the right focus, P is a point on the right branch of the hyperbola, P is above the X axis, and M is a point on the left quasilinear O is the origin of coordinates. OmpF is a parallelogram, | PF | = λ| of | (1) Find the relationship between eccentricity e and λ of hyperbola (2) If | ab | = 12, the hyperbolic equation at this time can be obtained (troublesome steps)
- 16. If the moving point P satisfies Po * Po = PA * Pb, the range of PA and Pb can be obtained A. B is the intersection point of a circle and X axis (Note: the origin of the circle is arbitrary), P is a moving point of the circle. The moving point P satisfies Po * Po = PA * Pb?
- 17. Given that the angle a = 60, P and Q are the moving points on both sides of angle a, if the sum of the lengths of AP and AQ is the fixed value 4, the minimum PQ of the line segment is obtained
- 18. Let p be a moving point on hyperbola x24-y2 = 1, o be the origin of coordinates, and m be the midpoint of line OP, then the trajectory equation of point m is______ ．
- 19. F1 and F2 are the two focal points of hyperbola, F1 is the focal point of parabola y ^ 2 = 4x, hyperbola passes a (- 2,0), B (2,0), find the trajectory equation of F2 Note the explanation of the value range of X Don't you know what to do?
- 20. The hyperbola C: 2x ^ - y ^ = 2 is known. Find the trajectory equation of the midpoint Q of the chord AB passing through the point m (2,1)