Question

For two vectors $A$ and $B$ which lie in a plane. Which of the following statement is correct?

• A. If magnitude of $A$ and $B$ vector is 3 and 4 and they add upto give vector having magnitude of 5 , then they must be perpendicular vector.
• B. If they add up to give more than 5 , then they must be inclined at obtuse angle.
• C. If they add upto give less than 5 , then they must be inclined at acute angle.
• D. None of the above

Answer 1

Answer: (A)

Since, $(5{)}^2=(3{)}^2+(4{)}^2$
which is in accordance to pythagoras theorem.
So, the vectors can be shown in the figure as
$\therefore A$ and $B$ are perpendicular.
However, if the length of $A+B$
vector is more than or less than $5$ , then they should be inclined at acute and obtuse angle, respectively.
Thus, the statement given in option is correct, rest are incorrect.