Question

if |vector A+ vector B|=|A|+|B| find the angle between A And B​

Answer 1

Answer:

Assuming A and B are vectors, there is a very well-known property, arising times and again in algebra, which is called the triangular inequality and states the following :

|A+B|≤|A|+|B|

It is in fact a fairly intuitive result if we think about the vectors of the three-dimensional Euclidian space (our simple and beloved and intuitive space) ; geometrically, you can obtain the sum of the two vectors by following the path traced by the vectors as you make the tip of the previous vector coincide with the tail of the next one.

So, if A and B are not aligned (colinear), you are going to obtain a triangle, hence the name : triangular inequality ! Now, the relation states that the length of the sum is smaller or equals to the sum of the length of the other two. What does our triangle look like if they are exactly equal ? Well, it doesn’t look like a triangle ; it looks like a straight-line, that is, the vectors must in fact be colinear in the end.

Meaning that they have the same direction, you obtain, finally, that the angle in this case must be zero.

Answer 2

Answer:

0°

Explanation:

we know that...

|A+B|^2 = |A|^2 + |B|^2 + 2|A| |B| cos @

but given that....

|A + B| = |A| + |B|

|A + B|^2 = [ |A| + |B| ]^2

|A + B|^2 = = |A|^2 + |B|^2 + 2|A| |B|

A|^2 + |B|^2 + 2|A| |B| cos@ = = |A|^2 + |B|^2 + 2|A| |B|

cos @ = 1

cos @ = cos 0°

therefore........

@ = 0°