Answer:
The scalars are s=-1 and t=5 such that sa+tb=<12,−18>
Step-by-step explanation:
Let a=<3,3> and b=<3,-3>, s and t are scalars such that sa+tb=<12,-18>
Let d be a scalar quantity and v=<a, b> be a vector quantity.
Now to multiply the vector v=<a, b> by the scalar quantity d, that is multiply each of its components by d as below:
d<a, b>=<ad,bd>
Given that sa+tb=s<3,3>+t<3,-3>
=<3s,3s>+<3t,-3t>
sa+tb=<3s+3t,3s-3t>
Now equating it to <12,-18> we get
3s+3t=12 and 3s-3t=-18
3(s+t)=12
s+t=4
s=4-t
Now substitute the value s=4-t in 3s-3t=-18 we get
3(4-t)-3t=-18
12-3t-3t=-18
-6t=-18-12
-6t=-30
Therefore t=5
And s=4-5=-1
Therefore s=-1 and t=5 such that sa+tb=<12,−18>