Question

If vectora + vectorb= vector c and a+ 2b is perpendicular to vector a find relation between magnitude of b and magnitude of c
NOTE : DON'T USE DOT PRODUCT

Answer 1

Here, a bold letter represents a vector.

Given: (a+b)•b =0.

So, a•b + b•b = 0

Multiplying by two on both sides,

We have: 2(a•b) + 2(b•b)= 0…….1️⃣

Also, it is given that (a+2b)•a =0.

So, a•a + 2(a•b) =0……..……2️⃣

So, doing 2️⃣-1️⃣, we have:

a•a - 2(b•b)=0

Which means,

a•a = 2(b•b)

As for any vector v, v•v = |v| 2,

Thus, |a| = √2 |b|.

Hope this helps!