NIMCET 2016 Question Paper with solutions

© examsiri.com

Question : 64 of 120

Marks: +1, -0

If a,b and a+b are vectors of magnitude α then the magnitude of vector a – b is;

$√2$ α
$√3$ α
$√3$ 2α
3α

Solution:

Given

|a|=|b|=|a+b|=α

∵|a+b|^2=|a|^2+|b|^2+2a⋅b

⇒α^2=α^2+α^2+2a⋅b

⇒a⋅b=-α^2/2

....(i)
Then,

|a-b|^2=|a|^2+|b^2|-2a⋅b

=α^2+α^2-2⋅(-α)^2/2

[From Eq. (i)]

=α^2+α^2+α^2

|a-b|^2=3α^2

⇒|a-b|=√{3α^2}

=√3α

© examsiri.com

Go to Question:

Prev Question

Next Question