Yr1 Vectors

Question 1

Gradient = …

Answer 1

… = Direction Vector

Question 2

To check if a point is co-linear (lies on the line)

Answer 2

Point = Line equation, if the values for λ are consistent, then they are co-linear

Question 3

r is…

Answer 3

(x,y)

Question 3

To convert to cartesian form…

Answer 3

look in the FG (can also be used for two-dimensions, just don’t include the z)

Question 3

If one of the direction vectors are 0, write it as…

Answer 3

x = …, (y-a2)/b2 = (z-a3)/b3
Whichever dimension is 0, would be a constant, and then you can write the other two in the for given in the FG

Question 4

If two of the direction vectors are 0, write it as…

Answer 4

x = …, y = …
You only need to write the two to describe the line. Whichever dimensions are 0 would both be constants.

Question 5

If vectors are perpendicular…

Answer 5

a . b = 0
If two vectors are given and you are proving that it is perpendicular to both, do the dot products with both to prove that they are perpendicular.

Question 6

To find the vector product…

Answer 6

Use the cross product
Note: To do this create a matrix with the first line being i, j and k, then find the determinant with i, j and k

Question 7

To find sin θ,

Answer 7

draw a right angled triangle and include the lengths of the modulus of vectors a and b

Question 8

Distance from origin to point (x,y,z)

Answer 8

Square root of x^2 + y^2 + z^2