Moderate -0.5 This is a straightforward application of the angle formula between two lines in vector form. Students need to recognize the y-axis direction vector (0,1,0), apply the dot product formula with the given line's direction vector, and calculate the acute angle. While it involves some arithmetic with surds, it's a standard technique with no conceptual challenges beyond direct formula application.
Correct direction vector representation of the y-axis.
1
Correct use of dot product with2 3 and their direction
− 3
vector for y-axis.soi
Correct use of dot product with their vectors to find cosine of
angle soi
. Condone eg. in place of .
2 2
�√3� �−√3�
3 π
Or cosϕ =− ⇒θ=π−ϕ= or 300 Accept 0.524c
2 6
Mark the final answer
SC B2 right answer only www
Question 4:
4 | Direction of y-axis is
0
�1�
1 0
0
2 3. 1 =2 3
− 3 0
2 3
cosθ=
( )2 ( )2
1× 1+ 2 3 + − 3
2 3
=
4
π
⇒θ= or 300
6 | B1
M1
M1
A1
[4] | 3.1a
1.1
1.1
1.1 | Correct direction vector representation of the y-axis.
1
Correct use of dot product with2 3 and their direction
− 3
vector for y-axis.soi
Correct use of dot product with their vectors to find cosine of
angle soi
. Condone eg. in place of .
2 2
�√3� �−√3�
3 π
Or cosϕ =− ⇒θ=π−ϕ= or 300 Accept 0.524c
2 6
Mark the final answer
SC B2 right answer only www