Question

given that vector A + vector B + vector C =0 . out of these three vectors two are equal in magnitude and the magnitude of the third vector is √2 times that of either of the two having equal magnitude. then the angles between the vectors are?​

Answer 1

Answer:

the three vectors may form triangle

so.

the angles may be

45 , 90 ,45

Answer 2

Answer:

135,135,90

Explanation:

90,135,135 are the angle between the vectors as  asked in the question while the angle between the triangles are 90,45,45.

Now, if we have to measure the angle between the vectors then we have to take the direction cosines to our use while taking the interior angles will give a wrong result.

As, in the question the vectors are given as A,B,C thus taking a triangle in which head of A touching tail of B and same goes for the rest.

Taking angles as x,y,z

Here,

A=B and C=$\sqrt{2}A=\sqrt{2}B$

$\frac{A}{sinx} =\frac{B}{siny}=\frac{C}{sinz}$

$\frac{A}{sinx}=\frac{C}{sinz}$

$\frac{A}{sinx} =\frac{\sqrt{2}A }{sin(180-(x+x))}$

$\frac{1}{sinx}=\frac{\sqrt{2} }{sin(2x)}$

$\frac{1}{sinx}=\frac{\sqrt{2} }{2sinxcosx}$

cosx=$\frac{1}{\sqrt{2} }$

x=45.

y=45.

z=90.

Thus angle bet A and B vector=180-z=90.

Thus angle bet B and C vector=180-x=135.

Thus angle bet C and A vector=180-y=135.