How do you find the acute angle between two intersecting lines whos equations are given in vector form?

For this question we first need to understand which angle it is we're calculating. When two lines intersect two pairs of equal and opposite angles are formed (4 angles total). We are looking to find the small of these two angle values.
To do this, we use the rearranged dot product formula. Only the direction parts of the line equations are needed - this is the part next to the scalar multiplier. We find the dot product of these two direction vectors as well as their magnitudes and then substitute these into the formula. Then we can use the inverse cosine function to give us the angle we're looking for.

Illustration of a video tutorial

Need help with Maths?

One to one online tuition can be a great way to brush up on your Maths knowledge.

Have a Free Meeting with one of our hand picked tutors from the UK’s top universities

Find a tutor

Related Maths A Level answers

All answers ▸

Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.


find the definite integral between limits 1 and 2 of (4x^3+1)/(x^4+x) with respect to x


C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.


Differentiate (2^x)(5x^2+5x)^2.


We're here to help

+44 (0) 203 773 6020support@mytutor.co.ukContact us
Facebook logoTwitter logoGooglePlus logoLinkedIn logo

© MyTutorWeb Ltd 2013–2021

Terms & Conditions|Privacy Policy