If the vectors a - i -2 j -3 k - and b -3 i -6 j - mk - are collinear- then m -

Given: nbsp;a #8594;=i^ 2j^+3k^ #160;and #160;b #8594;=3i^ 6j^+mk^ nbsp;are collinear The #160;vectors #160;a #8594;=i^ 2j^+3k^ #160;and ...

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Standard XII

Mathematics

Vector Triple Product

If the vector...

Question

If the vectors $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} a n d \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear, then m = ________________.

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Solution

Given: $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} and \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear

$The vectors \vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} and \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k} are collinear \Rightarrow \frac{1}{3} = \frac{- 2}{- 6} = \frac{3}{m} \Rightarrow \frac{1}{3} = \frac{3}{m} \Rightarrow m = 9$

Hence, m = 9.

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If the vectors a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear, then m = ________________.

Given: a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear The vectors a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear⇒13=-2-6=3m⇒13=3m⇒m=9 ​Hence, m = 9.

If the vectors $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} a n d \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear, then m = ________________.