How to find the acute angle between 2 equations?

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Can someone please explain to me how to do question 18? Thanks!

1 Answer
Ratnaker Mehta
Dec 7, 2017

# pi/4#.

Explanation:

Let the given lines be # l_1 : y=2x+4, and, l_2 : y=-3x+6.#

Let #m_1, and, m_2# be their respective slopes.

Clearly, #m_1=2, and, m_2=-3.#

If #alpha=/_(l_1,l_2) in [0,pi/2],# then, we have,

#tanalpha=|(m_1-m_2)/(1+m_1m_2)|,#

#=|(2-(-3))/(1+2(-3))|,#

#:. tanalpha=|5/-5|,#

# rArr alpha=arc tan 1=pi/4.#

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