Question

${What\:is\:the\:value\:of \:{\vec{AB}}\:+\:{\vec{BC}}\: \:{\vec{CD}}\:+\:{\vec{AD}}}$​

Answer 1

Answer:

TO FIND :

AB + BC + CD + AD

SOLUTION :

• We must know that, the direction of a vector is from its initial point to its final point

Therefore, direction of AB vector would be from A to B.

=> As A is considered the Initial Point and B is considered as the Final Point

Same goes for all vectors.

[Take help from the attachment now]

Let's rearrange the question as :-

• (AB+ BC) + (CD + AD)

For addition of 2 vectors :-

The resultant/ sum vector can then be obtained by joining the first vector’s tail to the head of the second vector.

• Condition necessary -

1. The first vector’s head must join the tail of the second vector.

• ∴ AB + BC = AC

As AC joins the first vector's (AB) head to the tail of the second vector.(BC)

∴ CD + AD

In this case the head of first vector(CD) does not join the tail of second vector (AD)

So displacing AD such that its tail joins the head of CD

[Check the attachment]

{Since, there's a new vector forming here, i have disturbed the points taken by you.}

Now, the vectors are suppose

CD and DG

[DG is the vector AD I've just named it differently now ,   please dont get confused (´。＿。｀)]

• CD + DG = CG

As CG joins the first vector's (CD) head to the tail of the second vector.(DG)

Now, adding AC and CG, to get the final resultant :-

• AC + CG = AG

As a new imaginary vector AG joins AC and CG.

Therefore the answer is CG.

                             

Hope this helps!