Christopher H.

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Degree: Mathematics (Bachelors) - Edinburgh University

Hi, I’m Chris, an undergraduate student studying Mathematics at Edinburgh University. I have always enjoyed tutoring almost as much as I enjoy maths, so I’m pretty enthusiastic about the combination of the two.

From helping my brother learn to tie a tie to tutoring GCSE science at my school, I have developed a patience and understanding of students’ needs.

The Sessions:

Being a university student, the difference between a tutorial and a lecture is clear to me. These sessions will be tutorials driven by the student with a focus on understanding the key concepts and ideas of the subject.

With this understanding, exam success (and enjoyment, I promise!) will come easily.

Other info:

I took the following A-level Maths/Further Maths modules on the OCR exam board:
C1,2,3,4
M1,2,3
S1,2
D1,2
FP1,2,3

I also did OCR Physics A at A-level.

If you have any questions for me, do not hesitate to send me a WebMail or book a 15 minute Meet the Tutor session.

I look forward to hearing from you!

#### Subjects offered

SubjectLevelMy prices
Further Mathematics A Level £20 /hr
Maths A Level £20 /hr
Physics A Level £20 /hr

#### Qualifications

MathematicsA-LevelA*
Further MathematicsA-LevelA
PhysicsA-LevelA
 CRB/DBS Standard No CRB/DBS Enhanced No

#### Ratings and reviews

4.5from 2 customer reviews

Vinita (Parent) March 16 2015

Brilliant, much clearer now.

Vinita (Parent) March 9 2015

Quite good lesson, would recommend it.
See all reviews

### How do I find the angle between 2 vectors?

First, we need to recall 2 basic definitions of vector operations: The dot product is defined on vectors u=[u1, u2,...un] and v=[v1, v2,..., vn] asu . v = u1v1+u2v2+...+unvn The length (norm) of a vector v=[v1, v2,..., vn] is the nonnegative scalar defined as||v||=√(v . v)=√(v12+v22+...+vn2) ...

First, we need to recall 2 basic definitions of vector operations:

The dot product is defined on vectors u=[u1, u2,...un] and v=[v1, v2,..., vn] as u . v = u1v1+u2v2+...+unvn
The length (norm) of a vector v=[v1, v2,..., vn] is the nonnegative scalar defined as ||v||=√(v . v)=√(v12+v22+...+vn2)

Note that u & v must be the same size to compute the dot product.

Now the formula for the angle, θ, between 2 vectors is as follows:

cos(θ)=(u . v)/(||u|| ||v||)

Notice that u & v can be any size so long as they are both the same size. That is, this formula can be used to find the angle between vectors in 2 dimensions and also to find the angle between vectors in 100 dimensions, however hard that is to imagine.

A handy rearrangement of that formula to isolate θ is:

θ=cos-1( (u . v)/(||u|| ||v||) )

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2 years ago

651 views
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