Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?

Correct result:

t₁ =  2
A₁ =  -38.6598 °
A₂ =  -128.6598 °
t₂ =  -3.125
B₁ =  51.3402 °
B₂ =  -128.6598 °

Solution:

$$\begin{gathered} 2t_x+5y-6=0 \\ 5x-4y+8=0 \\ {n}_1=(2t;5) \\ {n}_2=(5;-4) \\ normal \\ {n}_1\mathrm{.}{n}_2=0 \\ 2\cdot t_1\cdot 5+5\cdot (-4)=0 \\ 10t_1=20 \\ {t}_1=2 \end{gathered}$$

$A_1={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{5}{2\cdot t_1}}-90={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{5}{2\cdot 2}}-90=-38.6598^{\circ }=-38^{\circ }39^{\mathrm{\prime }}35\mathrm{"}$

$A_2={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{-4}{5}}-90=-128.6598^{\circ }=-128^{\circ }39^{\mathrm{\prime }}35\mathrm{"}$

$$\begin{gathered} parallel \\ {n}_1=k\cdot n_2 \\ k=5\mathrm{/}(-4)=-{\displaystyle \frac{5}{4}}=-1.25 \\ 2\cdot t_2=5\mathrm{/}(-4)\cdot 5 \\ 2t_2=-6.25 \\ {t}_2={\displaystyle \frac{-25}{8}}=-3.125=-{\displaystyle \frac{25}{8}} \end{gathered}$$

$B_1={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{5}{2\cdot t_2}}-90={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{5}{2\cdot (-3.125)}}-90=51.3402^{\circ }=51^{\circ }20^{\mathrm{\prime }}25\mathrm{"}$

$B_2={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan {\displaystyle \frac{-4}{5}}-90=-128.6598^{\circ }=-128^{\circ }39^{\mathrm{\prime }}35\mathrm{"}$

Try another example

Showing 0 comments:

Next similar math problems:

• Here is
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• Cuboids
  Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
• Three vectors
  The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
• Angle between vectors
  Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
• Scalar dot product
  Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
• Two forces
  The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• Forces
  Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
• Triangle
  Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
• Resultant force
  Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
• Three points 2
  The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
• Angle
  A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis.
• Flowerbed
  Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m² =
• Slope
  What is the slope of a line with an inclination 6.06 rad?
• Vector sum
  The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
• Cone
  The rotating cone volume is 9.42 cm³, with a height 10 cm. What angle is between the side of the cone and its base?
• Angle of the body diagonals
  Using vector dot product calculate the angle of the body diagonals of the cube.