Question

ABCD is an irregular quadrilateral. M is the midpoint of DC. vec (AB)=p,vec (AD)=q and vec (BC)=2p-3q Work out vec (DM) in terms of p and q.

Answer 1

To find vector DM, subtract vector DC from vector MC. Substitute the given values and simplify the equation to get vec (DM) = 3p - 6q.

Step-by-step explanation:

To find vector DM, we need to find the vector DC and subtract it from vector MC. Since M is the midpoint of DC, we can first find the vector DC by subtracting vector DM from vector DC:

vec(DC) = vec (DM) - vec (MC)

Next, we can substitute the given values into the equation:

vec (DC) = p - vec (MC)

vec (DC) = p - (2p - 3q)

vec (DC) = -p + 3q

Finally, we can subtract the result from vector MC:

vec (DM) = vec (MC) - vec (DC)

vec (DM) = (2p - 3q) - (-p + 3q)

vec (DM) = 3p - 6q