Question 48: Motion in 2D & Vectors

Question

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

Accepted Answer

$\vec{P} \,\&\, \vec{Q}$ are perpendicular
$$
\begin{aligned}
& \overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{Q}}=0 \\
& (\hat{\mathrm{i}}+2 \mathrm{~m} \hat{\mathrm{j}}+\mathrm{m} \hat{\mathrm{k}}) \cdot(4 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\mathrm{m} \hat{\mathrm{k}})=0 \\
& \Rightarrow 4-4 \mathrm{~m}+\mathrm{m}^2=0 \\
& \Rightarrow(\mathrm{m}-2)^2=0 \Rightarrow \mathrm{m}=2
\end{aligned}
$$

Answer

$$-1$$

Answer

3

Answer

1

Answer

2

Motion in 2D & Vectors

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

Choose the correct answer: