These are vectors as well:
(a) AB + __ = CA = 0
(b) AB +BC + CD + DA = __
the first was a mistake i wanted these ones. Complete these and please if you can, explain.
Looks to me like
AB + BC + CA = 0
Similarly for the other one. Getting back to A, the sum is just 0 again.
The vectors form a closed polygon, so the net result is zero.
If you want to use vector notation, then if the vector to A is a, and to B is b, etc.
Then
AB = b-a
BC = c-b
CA = a-c
AB+BC+CA = b-a+c-b+a-c = 0
AB is b-a because if there is a vector u such that a+u=b, then u=b-a.
Thanks this will help.
I only knew of:
AB + BC = AC(triangle rule)
and
AB + BC + CD = AC + CD = AD(parallelgram rule)
Suppose 4ABC has vertices A(−6, −2), B(−8, 0) and C(−4, 0):
Find AB, BC and CA. Show that their sum is a zero vector.
Sure! Let's break down these questions and explain how to find the missing vectors.
Question (a) states:
AB + __ = CA = 0
To find the missing vector, we can rearrange the equation as follows:
AB + __ = -CA
Since we know that the sum of two vectors is zero, we can deduce that the missing vector must be the negative of AB. Therefore, the missing vector is:
__ = -AB
So, to complete this equation, you can substitute the missing vector as -AB.
Moving on to question (b):
AB + BC + CD + DA = __
To find the missing vector, we need to sum up the given vectors: AB, BC, CD, and DA.
To add vectors, we add the corresponding components of each vector together. For example, for two-dimensional vectors like AB = (x1, y1) and BC = (x2, y2), the sum would be (x1 + x2, y1 + y2).
Similarly, you can add the components of each given vector together to find the vector sum AB + BC + CD + DA.
Once you perform the vector addition, you will obtain the missing vector that completes the equation. Simply write down the result as the missing vector:
__ = AB + BC + CD + DA
Now you have the missing vector for question (b).