The angle between the lines (x-5/7)=(y+2/-5)=(z/1) and (x/1)=(y/2)=(z/3) is

Question

The angle between the lines (x-5/7)=(y+2/-5)=(z/1) and (x/1)=(y/2)=(z/3) is (A) 0 (B) (π/2) (C) (π/3) (D) (π/4)

Tardigrade Admin · Accepted Answer

Direction ratios of the given lines are respectively 7, -5, 1 and 1, 2, 3. Now, a1 a2 + b1 b2 + c1c2 = (7)(1) + (-5)(2) + (1)(3) = 7 - 10 + 3 = 0 Therefore, the given lines are perpendicular.

Q. The angle between the lines $\frac{x - 5}{7} = \frac{y + 2}{- 5} = \frac{z}{1}$ and $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ is

$0$

$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

Direction ratios of the given lines are respectively $7$ , $- 5$ , $1$ and $1$ , $2$ , $3$ .
Now, $a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = (7) (1) + (- 5) (2) + (1) (3)$
$= 7 - 10 + 3 = 0$
Therefore, the given lines are perpendicular.

Q. The angle between the lines 7x−5​=−5y+2​=1z​ and 1x​=2y​=3z​ is

0

2π​

3π​

4π​

Direction ratios of the given lines are respectively 7, −5, 1 and 1, 2, 3. Now, a1​a2​+b1​b2​+c1​c2​=(7)(1)+(−5)(2)+(1)(3) =7−10+3=0 Therefore, the given lines are perpendicular.

Q. The angle between the lines $\frac{x - 5}{7} = \frac{y + 2}{- 5} = \frac{z}{1}$ and $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ is

$0$

$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{4}$

Direction ratios of the given lines are respectively $7$ , $- 5$ , $1$ and $1$ , $2$ , $3$ .
Now, $a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = (7) (1) + (- 5) (2) + (1) (3)$
$= 7 - 10 + 3 = 0$
Therefore, the given lines are perpendicular.