Respuesta :
Answer:
The value of m is [tex]-\frac83[/tex].
Step-by-step explanation:
If two vectors [tex]\vec A[/tex] and [tex]\vec B[/tex] are perpendicular to each other then their dot product will be zero i.e [tex]\vec A.\vec B=0[/tex]
If two vectors [tex]\vec A[/tex] and [tex]\vec B[/tex] are parallel to each other then their cross product will be zero i.e [tex]\vec A\times\vec B=\vec 0[/tex]
Given vectors are a= (3,4) and b=(m,2)
The position vector of [tex]\vec a[/tex] is =[tex]3 \hat i+4\hat j[/tex]
The position vector of [tex]\vec b[/tex] is =[tex]m \hat i+2\hat j[/tex]
Since [tex]\vec a[/tex] and [tex]\vec b[/tex] are perpendicular.
Then,
[tex]\vec a. \vec b=0[/tex]
[tex]\Rightarrow (3\hat i+4\hat j).(m\hat i+2 \hat j)=0[/tex]
⇒3.m +4.2=0
⇒3m+8=0
⇒3m= -8
[tex]\Rightarrow m=-\frac 83[/tex]
The value of m is [tex]-\frac83[/tex].
