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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
Because the vector of the line la-4 / 5 = B + 3 / 2 = C / 1 passing through the point (4, - 3,0) and M is: (4-3, - 3-1,0 - (- 2)) = (1, - 4,2) the direction vector of the line is (5,2,1) let the plane vector be n, then n = the cross product of the two vectors = | I j K1 - 4 25 2 1 | = (- 8,9,22) the plane equation is: - 8 (x-3) + 9 (Y-1
Find the linear equation which passes through the point m (1,2,3) and is perpendicular to the plane 2x + y-3z + 5 = 0
First find the direction vector of the line, that is, the normal vector of the plane (2,1, - 3)
(X-1)/2=(Y-2)/1=(Z-3)/-3
The equation of the plane passing through point (2, - 1,0) and parallel to the straight line (x + 3) / 2 = (Y-1) / 3 = (Z + 2) / - 1 is as follows:
(x-2)/2=(y+1)/3=z/-1
There are two points a (- 1,0) and B (1,0) on the plane. Point P is on the circle (x-3) & sup2; + (y-4) & sup2; = 4 to find the minimum value of AP & sup2; + BP & sup2
The following 3x = 4Y can not be obtained by substituting
Let the symmetric point of point P about the origin be q, then the quadrilateral apbq is a parallelogram, and the sum of squares of the four sides of the parallelogram is equal to the sum of squares of its diagonal, that is: 2 (AP & sup2; + BP & sup2;) = AB & sup2; + PQ & sup2; = 4 + 4 (OP) & sup2;, so AP & sup2; + BP & sup2; = 2 + 2op & sup2;, so only the minimum value of OP & sup2; is required, The location of the minimum OP is the intersection of the line between the origin and the center of the circle
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. 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?
- 4. 1995-1+2-3+4-5+… +1948-1949=______ ．
- 5. 1995-1+2-3+4-5+… +1948-1949=______ ．
- 6. 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
- 7. 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
- 8. It is known that the vertex of the parabola is at the origin and the focus is the focus of the hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1
- 9. Find the normal vector of the plane passing through points a (0,0,0), B (1,4,0), C (0,2,0)
- 10. As shown in the figure, in ▱ ABCD, if the bisector AE of ∠ bad intersects BC at e, ad = 6, EC = 2, then the length of CD=______ ．
- 11. 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
- 12. If a line passes through point m (a, 3) and point n (1, 2), the equation of the line is solved
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. 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
- 18. 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)
- 19. 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?
- 20. 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