Question

two vectors a and b are equal in magnitude but perpendicular to each other assuming a suitable scale represent their following combination a+2b, a-2b, 2a-b, b-1/2a​

Answer 1

Given:

Two vectors a and b are equal in magnitude but perpendicular to each other.

To Find:

Assuming a suitable scale represent their following combination a+2b, a-2b, 2a-b, b-1/2a​?

Solution:

it is given that , two vectors a and b are equal in magnitude but perpendicular

to each other.

therefore, a =  b and θ = 90 degree :angle between a and b.

so, according to question, we have

for, a+2b;

$r = \sqrt{a^2+(2b)^2+4abcos(\pi/2)}\\\\r=\sqrt{a^2+(2a)^2+4ab\times0}\\\\r=\sqrt{5}a \ or \ \sqrt{5}b$

for, a-2b

$r=\sqrt{5} \ a \ or \ \sqrt{5}b$

for , 2a-b

$r=\sqrt{5} \ a \ or \ \sqrt{5}b$

for, b-(1/2)a

$r=\sqrt{3/2}a \ or \ \sqrt{3/2} b$