Three vectorsA,B,Csuch thatvectorA=vectorB+vectorC their magnitude are5,4,3findtheangle between vectorA andC

physics chapter vector

As per vector addition A^2=B^2+C^2+2BxCx cos @ where @=angle between B & C.
or cos @= (A^2-B^2-C^2)/2xBxC
= (5^2-4^2-3^2)/2x4x3
=0

So @=90deg

Now tan$= B sin@/(C+B cos@) where $=angle between A and C

or tan$= B/C since @=90deg

=4/3
or $=tan inverse 4/3=53 deg

As
A = B + C

in vector addition, A is the resultant of B and C,means hyp,
so for a right angle triangle

a(sq) = b(sq) + c(sq) whole under root,,,

so its a right angle,90

Vectors B and C are the legs of a 3-4-5 right triangle; they sum to a vector of magnitude 5 (vector A).
The angle between A and C is tanˉ¹(4/3), about 53°.

90 degrees