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Scalar Or Dot Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product2 Marks
Question
If the vectors $3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}$ and $18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}$ are parallel, find the value of m.
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Answer

THe given vectors are parallel.
$\therefore3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}=\text{t}\big(18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}\big)$
$\Rightarrow3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}=18\text{t}\hat{\text{i}}-12\text{t}\hat{\text{j}}-\text{t}\text{m}\hat{\text{k}}$
Comparing both sides, we get
$18\text{t}=3,-12\text{t}=-2,-4=\text{tm}$
$\Rightarrow\text{t}=\frac{1}{6}$
Substituting the value of m in -4 = -tm, we get
$-4=-\text{m}\big(\frac{1}{6}\big)$
$\therefore\text{m}=24$

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