Question

prove that vectors A=2i^-3j^-k^ and B=-6i^+9j^+3k^ are parallel to each other

Answer 1

Given:

Two vectors are $\vec{A}=2\hat{i}-3\hat{j}-\hat{k}$ and $\vec{B}=-6\hat{i}+9\hat{j}+3\hat{k}$.

To prove:

That the given vectors are parallel.

Prove:

Two vectors $\vec{u}$ and $\vec{v}$ are parallel, if

$\vec{u}=\lambda \vec{v}$

where, $\lambda$ is a non zero constant.

We have,

$\vec{A}=2\hat{i}-3\hat{j}-\hat{k}$

$\vec{B}=-6\hat{i}+9\hat{j}+3\hat{k}$

It can be written as

$\vec{B}=-3(2\hat{i}-3\hat{j}-\hat{k})$

$\vec{B}=-3\vec{A}$

$-\dfrac{1}{3}\vec{B}=\vec{A}$

$\vec{A}=-\dfrac{1}{3}\vec{B}$

Here, $\lambda=-\dfrac{1}{3}$.

Since, $\vec{A}=\lambda \vec{B}$ where, $\lambda=-\dfrac{1}{3}$, therefore, both vectors A and B are parallel.

Hence proved.

Answer 2

hope its help uh..

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