If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ - 2 j ^ + m k ^ are perpendicular to each other. Then, the value of m will be

Question

If two vectors P &#8594; = i ^ + 2 m j ^ + m k ^ and Q &#8594; = 4 i ^ - 2 j ^ + m k ^ are perpendicular to each other. Then, the value of m will be

Aicharya · Accepted Answer

For two vectors to be perpendicular, their dot product is equal to zero.

So, $\vec{P} \cdot \vec{Q} = 0$

$\Rightarrow (\hat{i} + 2 m \hat{j} + m \hat{k}) \cdot (4 \hat{i} - 2 \hat{j} + m \hat{k}) = 0 \Rightarrow 4 - 4 m + m^{2} = 0 \Rightarrow {(m - 2)}^{2} = 0 \Rightarrow m = 2$

If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ - 2 j ^ + m k ^ are perpendicular to…

Solution

If two vectors P &#8594; = i ^ + 2 m j ^ + m k ^ and Q &#8594; = 4 i ^ - 2 j ^ + m k ^ are perpendicular to…

Solution

If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ - 2 j ^ + m k ^ are perpendicular to…