Acute angle between the lines (vectors) (KristaKingMath)

Learn how to find the acute angle between two lines using vector representations of both lines. Remember that the acute angle is the angle which is less than 90 degrees. If two lines intersect each other and are anything other than perpendicular, then the intersection creates two equal obtuse angles and two equal acute angles. The acute angle is the one we learn to find in this video.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[kylahkropp]

i was so confused why i was wrong but you made it obvious that if we found an answer greater than 90 degrees that it was the obtuse one we found and we needed to subtract it from 180. saved me from a headache, thank you. also the fact you pointed out that the calculator needs to be in degrees (or radians if asked for radians). those last two tips were huge mentions that people could easily forget to say

[AmoraBrown]

This was great. You explained this very well. Thank you! :)

[GodsonSamuel]

Thanks for the help. It was quite informational. Much appreciated.

[osmankhalil]

if i use the slope to get another point beside (0, 7) for the second equation, i get this point ( 1, 4) >> and if i use these two points to figure the direction of the line ( direction vector) i get <1, -3) not <3, 1> which are pointing in different dircctions

[varnikdas]

Thank you for this❤️ I'm getting help from these videos ☺️

[SirCampsalot]

Thanks so much. Funny enough, this was the exact question for our homework when I was just searching for a random example.

[noahd]

why do the coefficients of x and y represent the vectors x and y components respectively? this does not make sens to me, as the slop of the lines would indicate the direction of the vector, and the other information just has to do with its location, which is irrelevant in this case. There for shouldn't the vector that represented the line y=2x-3 be <1, 2> and the vector that would represent y=-3x+7 would be <-1, 3>?

[lorenzorosales]

Great explanation!!!!
Thank you Krista King

[mikem]

Do you mind explaining or proving how using the coefficients in the equations are used to create the vectors?

[irinafranke]

Krista, what do your vectors <2, -1> and <3, 1> represent (speaking of the 2 given lines)?

[reals.]

than you, you explain so well ! way better than Khan academy

[omaranwer]

should we take the absolute value of the dot product if we want to get the acute angle ?

[chrisburgess]

Very nicely explained, thank you. As I worked along I came up with a question: at the beginning we converted to slope-intercept form, but for the calculations we used the original form from the problem. Did you change to S-I form just make to the graph? If I'm not mistaken, this can be solved without the graph, right? (although I like seeing what I'm doing!)

[KampungJering]

Hi, one question, if the question does not state that you need to find an acute angle, it just says find the angle, and my final answer is more than 90 degrees and less than 180 degrees, should I just leave it or I have to use 180 degrees subtract my answer to get the acute angle? Thanks!

[rasiel]

How did you get √50 as your denominator?

[kaylacarin]

So what if I am given 2 lines in y= form? I can't just get their coefficients anymore...