a and b are perpendicular vectors.a=(2i+3j) and b=ti+dj(d>0 and i and j are unit vectors) and |b|=1

Question

Find t and d?

I know we have to use the cross product here.

a.b=|a||b|*cos(π/2)
(2i+3j)(ti+dj)= √13*1*0
2t+3j=√13*0
How do we find t and d?

Answer 1

As you say, we need

a•b = 0
2t+3d = 0

but b is also a unit vector, so
t^2+d^2 = 1

Solving those two equations gives the values of t and d. Pick the solution where d>0.

Answer 2

Thanks Steve!