csat-suneung 2022 Q25 (Geometry)

csat-suneung · South-Korea · csat__math 3 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines

In the coordinate plane, consider two lines $$\frac { x + 1 } { 2 } = y - 3 , \quad x - 2 = \frac { y - 5 } { 3 }$$ If $\theta$ is the acute angle between these lines, what is the value of $\cos \theta$? [3 points]
(1) $\frac { 1 } { 2 }$
(2) $\frac { \sqrt { 5 } } { 4 }$
(3) $\frac { \sqrt { 6 } } { 4 }$
(4) $\frac { \sqrt { 7 } } { 4 }$
(5) $\frac { \sqrt { 2 } } { 2 }$

In the coordinate plane, consider two lines
$$\frac { x + 1 } { 2 } = y - 3 , \quad x - 2 = \frac { y - 5 } { 3 }$$
If $\theta$ is the acute angle between these lines, what is the value of $\cos \theta$? [3 points]\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { \sqrt { 5 } } { 4 }$\\
(3) $\frac { \sqrt { 6 } } { 4 }$\\
(4) $\frac { \sqrt { 7 } } { 4 }$\\
(5) $\frac { \sqrt { 2 } } { 2 }$

Paper Questions