find the vector having a length 5m in the XY plane that is perpendicular to vector A =(3i^+4J^-2k^) ?

vector A =(3i^+4J^-2k^),

 

let the required vector is B = x i^ + y j^

 

sqrt (x² + y²) = 5, 

 

x² + y² = 25  ..............(1)

 

Since vector A and B are perpendicular to each other then,

 

A.B = 0

 

3x + 4 y = 0

 

y = -3x/4 ..............(2)

 

Solving these two equations we get x = 4 and y = -3;

 

hence vector B = 4 i^ -3 j^