If a vector A-2-2-3k- and B-3-6-nk- are perpendicular to each other- then the value of n is

Solve for the required valueGiven, the vectors are A=2î+2ĵ+3k̂ and B=3î+6ĵ+nk̂ and that they are perpendicular.We know that, if two vectors are perpendicular, t ...

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Byju's Answer

Standard XII

Mathematics

Distance between Two Parallel Planes

If a vector A...

Question

If a vector $\vec{A} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $\vec{B} = 3 \hat{i} + 6 \hat{j} + n \hat{k}$ are perpendicular to each other, then the value of $n$ is

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Solution

Solve for the required value
Given, the vectors are $\vec{A} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $\vec{B} = 3 \hat{i} + 6 \hat{j} + n \hat{k}$ and that they are perpendicular.
We know that, if two vectors are perpendicular, then their dot product is $0$
Dot product of two vectors $\vec{P} = x_{1} \hat{i} + y_{1} \hat{j} + z_{1} \hat{k}$ and $\vec{Q} = x_{2} \hat{i} + y_{2} \hat{j} + z_{3} \hat{k}$ is given as,
$\vec{P} \cdot \vec{Q} = x_{1} \cdot x_{2} + y_{1} \cdot y_{2} + z_{1} \cdot z_{2}$
Here, $(x_{1}, y_{1}, z_{1}) = (2, 2, 3)$ and $(x_{2}, y_{2}, z_{2}) = (3, 6, n)$
Thus,
$\begin{matrix} 2 \times 3 + 2 \times 6 + 3 \times n = 0 \\ \Rightarrow & 6 + 12 + 3 n = 0 \\ \Rightarrow & 3 n = - 18 \\ ∴ & n = - 6 \end{matrix}$
Hence, the value of $n$ is $- 6$ .

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If a vector A→=2i^+2j^+3k^ and B→=3i^+6j^+nk^ are perpendicular to each other, then the value of n is

If a vector $\vec{A} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $\vec{B} = 3 \hat{i} + 6 \hat{j} + n \hat{k}$ are perpendicular to each other, then the value of $n$ is