Question

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

(a) 1/4  (b) 1/8  (c) 1 (d) 2.
Pls solve the question and also give the reason for every step.​

Answer 1

Answer:

(c) 1 ,(d) 2

Explanation:

This question is of multiple type.(more than one correct)

1) 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)

Answer 2

Answer:

c and d is correct

Explanation:

This question is of multiple type.(more than one correct)

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

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

So, Value of a/b may be 1 or 2.

Option (C) ,(D)