Angle Between Lines/Planes/Line and Plane

Submitted by vladimir.arzt on Wed, 07/10/2024 - 15:15

Project ID:

7200000046

Accepted:

SubArea:

Type:

Layout:

Question:

Match each set of equations describing two lines, two planes, or a line and plane with the correct measure of the angle between them.

Questions Title:

Lines and Planes

Answers Title:

Angles

Question 1:

\begin{array}{lllll} p : & x = 3 + t, & y = - 2 + 3 t, & z = 2 + 4 t, & t \in R, \\ q : & x = - 4 + 3 s, & y = 5 - 4 s, & z = 1 - s, & s \in R . \end{array}

Answer 1:

60^{\circ}

Question 2:

\begin{aligned} p : x = 1 - 3 t, y = - 2 + 4 t, z = 1 + 2 t, t \in R, \\ β : 2 x - y + 5 z - 9 = 0. \end{aligned}

Answer 2:

0^{\circ}

Question 3:

\begin{aligned} α : x - 2 z + 2 = 0, \\ β : 3 y + 1 = 0. \end{aligned}

Answer 3:

90^{\circ}

Question 4:

\begin{aligned} α : 3 x - 2 = 0, \\ q : x = - 4 + t, y = 7, z = 1 - t, t \in R . \end{aligned}

Answer 4:

45^{\circ}

Answer 5:

$150^{\circ}$

Answer 6:

30^{\circ}

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