Question

if a=3i+4j+mk is perpendicular to b=2i-j+4k,then value of m is​

Answer 1

For two vectors to be perpendicular-

a.b=0

⟹(2i+mj−3k).(i−2j+k)=0

⟹2−2m−3=0

⟹m= -1/2

hope it helps you ☺️

Answer 2

Given data: $a=3i+4j+mk$ is perpendicular to $b=2i-j+4k$

To find: The value of m.

Solution:

• The two perpendicular vectors uses dot product.
• The product of two vectors is the dot product.
• The dot product of the two given vectors can be denoted as, $a.b=0$
• $(3i+4j+mk).(2i-j+4k)=0$
• Now, combine the like terms
• $(3i.2i)+(4j.(-j))+(mk.4k)=0$
• Separate the vectors,
• $6(i.i)-4(j.j)+4m(k.k)=0$
• $6-4+4m=0$, since $i.i=j.j=k.k=1$
• Simplify the values,
• $2+4m=0$
• $4m=-2$
• $m=\frac{-2}{4}$
• $m=\frac{-1}{2}$
• Therefore, the value of m is $\frac{-1}{2}$