If \overrightarrow{a} and \overrightarrow{b} are two vectors such that |\overrightarrow{a}|=3, |\overrightarrow{b}|=4, |\overrightarrow{a}+\overrightarrow{b}|=1, then the value of |\overrightarrow{a}-\overrightarrow{b}| is:

NIMCET 2025 Paper

Section: Mathematics

Question : 32 of 120

Marks: +1, -0

{a}↖{→}

and

{b}↖{→}

are two vectors such that

|{a}↖{→}|=3, \;\; |{b}↖{→}|=4, \;\; |{a}↖{→}+{b}↖{→}|=1,

then the value of

|{a}↖{→}-{b}↖{→}|

is:

Solution:

|{a}↖{→}+{b}↖{→}|^2=a^2+b^2+2 a b \cos θ=1

9+16+24 \cos θ=1

24 \cos θ=-24 ⇒ \cos θ=-1

So the vectors are in opposite directions, and

|{a}↖{→}-{b}↖{→}|=|3+4|=7

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