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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..)

Here is the explanation that was provided: (but I don't understand it..) Can anyone please help?

 May 15, 2022
 #1
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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
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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
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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
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Ooh I kind of see the idea now! Thanks!!

Guest May 15, 2022

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