+0

0
121
4

The answers are a=1 and a=49/23

However, I do not understand why a=1 is an accepted answer (Because If we substituted a=1 in the scalar product of the two direction vectors, it gives a negative answer so cos(angle) = -ve ----->The angle is obtuse??? (The question stated that the angle is acute..)

May 15, 2022

#1
+9461
0

It is correct since the angle could be $$180^\circ - \cos^{-1}\left(\dfrac16\right)$$. Having a $$x^\circ$$ angle is basically the same thing as having a $$(180 - x)^\circ$$ angle.

May 15, 2022
#2
0

Sorry, but how is having a "x" angle the same as 180-x ?
(If x=60 then it is acute, but 180-60 = 120 is obtuse?)

Guest May 15, 2022
#3
+9461
0

We always use the acute angle to describe the angle between two lines. That's why when we have a 120-degree angle between the lines, we calculate the angle adjacent to it and conclude that the lines form an angle of 60 degrees.

MaxWong  May 15, 2022
#4
+1

Ooh I kind of see the idea now! Thanks!!

Guest May 15, 2022