Question

let a and b be two non null vectors such that |a+b|=|a-2b| . Then the value of |a|/|b| May be : ​

Answer 1

Answer:

Explanation:We have, two non null vectors 'a' and 'b' such that :

|\vec{a}+\vec{b}|=|\vec{a}-2\vec{b}|\\ \\=>|\vec{a}+\vec{b}|^2=|\vec{a}-2\vec{b}|^2\\ \\=>|\vec{a}|^2+|\vec{b}|^2+2|\vec{a}||\vec{b}|cos(\theta)=|\vec{a}|^2+4|\vec{b}|^2-2*|\vec{a}||\vec{2b}|cos(\theta)\\ \\=>3|\vec{b}|^2=6|\vec{a}||\vec{b}|cos(\theta)\\ \\=>cos(\theta)=\frac{|\vec{b}|}{2|\vec{a}|}\\ \\=>\frac{1}{2} \leq \frac{|\vec{a}|}{|\vec{b}|}=\frac{1}{2cos(\theta)} <\infty

Since, 1>1/2 , 2>1/2.

So, Value of a/b  may be 1 or 2.

Option (C) ,(D)

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