What is the vector in the xy-plane through origin and perpendicular to the vector `vec(r)=a vec(i) +b hat(j)` and of the same length?

What is the vector in the XY -plane through origin and perpendicular to the vector vec(r )= a hat(i) +b hat(j) and of the same length?

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

A plane is at a distance of 5 units from the origin and perpendicular to the vector 2hat(i) + hat(j) + 2hat(k) . The equation of the plane is a) vec(r ).(2hat(i) + hat(j) -2hat(k))=15 b) vec(r ).(2hat(i)+ hat(j)-hat(k))=15 c) vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15 d) vec(r ).(hat(i) + hat(j) + 2hat(k))=15

Find a vector whose length is 7 and that is perpendicular to each of the vectors vec(A) = 2 hat(i) - 3 hat(j) + 6 hat(k) and vec(B) = hat(i) + hat(j) - hat(k)

Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors parallel and perpendicular to the vector vec(a) = hat(i) + hat(j) .

Find the vector whose length is 3 and which is perpendicular to the vectors vec a=3 hat i+hat j-4 hat k , vec b=6 hat i+5 hat j-2 hat k .

Find a vector whose length is 3 and which is perpendicular to the vector vec a=3hat i+hat j-4hat k and vec b=6hat i+5hat j-2hat k