Explanation
To find the angle α between two lines, we use the formula for the angle between lines with slopes m1 and m2:
tanα=1+m1m2m1−m2
Step 1: Find the slope of the given line L
The equation of the line L is x+3y+33=0.
Rewriting it in the slope-intercept form (y=mx+c):
3y=−x−33
y=−31x−3
Thus, the slope m1=−31.
Step 2: Find the slope of the second line
The second line is x−3y=0.
Rewriting it:
3y=x
y=31x
Thus, the slope m2=31.
Step 3: Calculate the angle α
Substitute the slopes into the angle formula:
tanα=1+(31)(−31)31−(−31)
tanα=1−3132
tanα=3232
tanα=32⋅23
tanα=33=3
Since tanα=3, we have:
α=60∘
Correct Option: (c) 60∘
