![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given the vertices a (1, - 1,2), B (5, - 6,2) C (1,3, - 1) of △ ABC, then the length of high BD on the edge of AC is (vector)
Let D (x, y, z), due to the equation of AC
(x-1)/0=(y+1)/4=(z-2)/-3=t
The parameter equation is x = 1, y = 4t-1, z = - 3T + 2, so D (1,4t-1, - 3T + 2)
Because vector AC = (0,4, - 3)
BD=(x-5,y+6,z-2)=(-4,4t+5,-3t)
AC perpendicular to BD
therefore AC.BD=0
4*(4t+5)-3*(-3t)=0
16t+9t+20=0
t=-4/5
So BD = (- 4,9 / 5,12 / 5)
The length of high BD is | BD | = (16 + 81 / 25 + 144 / 25) ^ 1 / 2 = (16 + 225 / 25) ^ 1 / 2 = (16 + 9) ^ 1 / 2 = 5
RELATED INFORMATIONS
- 1. If the vertices a (1. - 1,2), B (5, - 6,2) C (1,3, - 1) of △ ABC are known, then the length of high BD on the edge of AC is equal to
- 2. In the triangle ABC, the angle ABC is the acute angle, the point D is the moving point on the ray BC, connecting ad, and making a square ADEF on the right side of ad with AD as one side If AB = AC and BAC = 90, is CF perpendicular to BD when point D is on the extension line of BC? If AB is not equal to AC angle, BAC is not equal to 90 point D, then BC motion triangle ABC satisfies what condition CF is perpendicular to BC If AC = 4, radical 2, BC = 3, under the condition of 2, let CF intersection of square ADEF and P find the maximum value of CP
- 3. In the triangle ABC, point D is a point on the ray Ba, make de = CD, intersect the straight line BC at point E. when point D is on AB, find CE = AD + AC These triangles are equilateral
- 4. In the triangle ABC, the angle ACB is the acute angle, the point D is the moving point on the ray BC, connecting ad, and making a square ADEF with AD as one side and on the right side of AD
- 5. As shown in the figure, two congruent right triangles are overlapped, and one of them is translated to the position of △ def along the direction from point B to C, ab = 10, do = 4, and the translation distance is 6, then the shadow area is () A. 48B. 96C. 84D. 42
- 6. Given that the coordinates of the three vertices of the triangle ABC are a (- 2,1), B (3,6), C (6,5), the equation of the circumcircle of the triangle ABC is obtained
- 7. Given that the vertex coordinates of ABC are a (- 1,2,3) B (2, - 2,3) and C (1 / 2,5 / 2,3), the shape of ABC is
- 8. In △ ABC, the opposite sides of angles a, B and C are a, B and C respectively, and satisfy 2bcosa = ccosa + acosc. (1) find the size of angle a; (2) if a = 3 and s △ ABC = 334, try to judge the shape of △ ABC and explain the reason
- 9. Given that the vertices of triangle ABC are a (1,2). B (2,3). C (- 2,5), then what kind of triangle is a triangle? A right angle, B acute angle, C Angle, not above D It's better to have an analysis process
- 10. Given the coordinates of the three vertices of the triangle 2.11.03.0, the sine value of the ball angle B and the area of the triangle
- 11. It is known that the vertex of triangle ABC is a (0,1) B (8,0) C (4,10) if vector BD = vector DC, and vector CE = 2, vector EA, a The intersection of AD and be is f, and the vector AF is obtained.
- 12. In ABC, a > C > b, and C = a + B / 2, if vertex a (- 1,0) B (1,0), find the trajectory equation of vertex C
- 13. In △ ABC, a > b > C, and C = (a + b) / 2, if vertex a (- 1,0), B (1,0), find the trajectory equation of vertex C
- 14. What graph does the equation x = e ^ t + e ^ - t, y = e ^ t + e ^ - t (t is a parameter) represent Why a hyperbola x ^ 2-y ^ 2 = 4 instead of a straight line x = y
- 15. It is known that the parabola y = x ^ 2 + 2x + m intersects with X axis at two points AB, and the equation of a circle with diameter AB is obtained
- 16. If there is a common point between the line L passing through point a (3,0) and the curve (x-1) 2 + y2 = 1, then the value range of the slope of the line L is () A. (−3，3)B. [−3，3]C. (−33，33)D. [−33，33]
- 17. In RT triangle ABC, angle c = 90 degrees, angle a = 45 degrees, and ab = 8 AC.BC
- 18. Point P and point q are on the line AB, and AP: Pb = 3:2, AQ: QB = 3:4, PQ = 3, find the length of line AB?
- 19. Try to discuss the application of Maslow's hierarchy of needs theory in management
- 20. Schematic diagram of lever principle in push up Push up is a hard lever, please draw the arm and fulcrum, dynamic resistance