Vectors a=[-3,2] and vector b=[6,t-2]. Determine t so that a and b become parallel?

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Vectors a=[-3,2] and vector b=[6,t-2]. Determine t so that a and b become parallel?

I really appreciate some help :)

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Answer 1 · 2018-04-21T03:51:03

Since $\to a$ $veca$ and $\to b$ $vecb$ originate form origin ; if they are parallel then $\to b$ $vecb$ must be a generated from $\to a$ $veca$
$i e$ $ie$ $\to b$ $vecb$ is a scalar multiple of $\to a$ $veca$ .

Explanation:

So $\to b = λ \to a$ $vecb = lambdaveca$ ; { $λ$ $lambda$ is some scalar}

$\Rightarrow [6, t - 2] = λ [- 3, 2]$ $rArr[6,t-2]=lambda[-3,2]$

$\Rightarrow [6, t - 2] = [- 3 λ, 2 λ]$ $rArr[6,t-2]=[-3lambda,2lambda]$

$\Rightarrow 6 = - 3 λ \Rightarrow λ = - 2$ $rArr 6=-3lambda rArr lambda = -2$

And now $t - 2 = 2 λ \Rightarrow t - 2 = - 4$ $t-2=2lambda rArr t-2 = -4$

$:.t=-2$

Finally $vecb=[6,-4]$ and it is parallel to $veca$ .

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Vectors a=[-3,2] and vector b=[6,t-2]. Determine t so that a and b become parallel?

I really appreciate some help :)

1 Answer

Explanation:

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