AS Maths Vectors - Help needed !

Why does the answer say p = 8 and q = +/- 6
Why can't p = +/- 8

Why does the answer say p = 8 and q = +/- 6
Why can't p = +/- 8

you are correct. p can be positive or negative, q must be positive.

Can someone pls explain ??

you are correct. p can be positive or negative, q must be positive.

I don't know what phrasing they use in modern exam papers, but having read the question about 4 times now, I can see two possible ways of interpreting it:

1) the angle theta is an acute angle either above or below the positive x-axis with sin(theta) = 3/5, i.e. it represents the size of the angle, not its direction. In this case p ,must be positive but q can be positive or negative;

2) the angle theta is being measured in a positive sense from the positive x-axis, in which case there is one solution with acute theta (i.e. p positive, q positive) and one solution with obtuse theta (i.e. p negative, q positive).

I must admit my first reading of the question led me to solution 1, However, having now looked at the third screenshot you posted they seem to have drawn a diagram corresponding to interpretation 2, but listed the solutions corresponding to interpretation 1. Then they've gone ahead and said actually we can have 4 solutions by symmetry!!

Is this from a textbook or a made-up set of problems?

I don't know what phrasing they use in modern exam papers, but having read the question about 4 times now, I can see two possible ways of interpreting it:

1) the angle theta is an acute angle either above or below the positive x-axis with sin(theta) = 3/5, i.e. it represents the size of the angle, not its direction. In this case p ,must be positive but q can be positive or negative;

2) the angle theta is being measured in a positive sense from the positive x-axis, in which case there is one solution with acute theta (i.e. p positive, q positive) and one solution with obtuse theta (i.e. p negative, q positive).

I must admit my first reading of the question led me to solution 1, However, having now looked at the third screenshot you posted they seem to have drawn a diagram corresponding to interpretation 2, but listed the solutions corresponding to interpretation 1. Then they've gone ahead and said actually we can have 4 solutions by symmetry!!

Is this from a textbook or a made-up set of problems?

I don't know what phrasing they use in modern exam papers, but having read the question about 4 times now, I can see two possible ways of interpreting it:

1) the angle theta is an acute angle either above or below the positive x-axis with sin(theta) = 3/5, i.e. it represents the size of the angle, not its direction. In this case p ,must be positive but q can be positive or negative;

2) the angle theta is being measured in a positive sense from the positive x-axis, in which case there is one solution with acute theta (i.e. p positive, q positive) and one solution with obtuse theta (i.e. p negative, q positive).

I must admit my first reading of the question led me to solution 1, However, having now looked at the third screenshot you posted they seem to have drawn a diagram corresponding to interpretation 2, but listed the solutions corresponding to interpretation 1. Then they've gone ahead and said actually we can have 4 solutions by symmetry!!

Is this from a textbook or a made-up set of problems?

so the angle could be measured anticlockwise from the positive x direction ( which is what we are used to ), or clockwise.

the results from the two cases are linked by a reflection in the x axis. for the first case p = + or - 8 and q = 6

for the second case p = + or - 8 and q = - 6