Does anyone know the answer for this please?

Your teacher didn't put any xy axis on this grid. But I'm assuming that the vectors are coming from the origin (0,0)

If that is the case, then vector v = (-2,4) and vector u = (2,1)

Add the corresponding coordinates to get

v+u = (-2,4)+(2,1) = (-2+2,1+4) = (0,5)

The general rule for adding vectors is

if u = (a,b) and v = (c,d), then u+v = (a+c, b+d)

TS is 24 units

Explanation:

ΔTRS and ΔSTQ are right angle triangle

Using pythagoras theorm:

(3x)² = (TR)² + (12)²

(3x)² = (18)² - (QT)²

(18)² - (QT)² = (TR)² + (12)²

180 = (TR)² + (QT)²

36 = (QT)² - (TR)²

QT² = 144

QT = 12

ΔTRS and ΔQRT are similar

Therefore, TS is 24 units