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For what value of a, the vectors (2i− 3j+ 4k) and (ai+ 6j− 8k) are collinear? |
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Answer» Direction ratios of vectors (\(2\hat i-3\hat j+4\hat k\)) and (\(a\hat i+6\hat j-8\hat k\)) are 2, −3, 4 and a, 6, −8, respectively. The vectors \((2\hat i-3\hat j+4\hat k)\) and \((a\hat i+6\hat j-8\hat k)\) are collinear if \(\cfrac2a=\cfrac{-3}6=\cfrac{4}{-8}\) ⇒ \(\cfrac2a=-\cfrac12\) ⇒ a = -4. If a = −4 then the vectors \((2\hat i-3\hat j+4\hat k)\) and \((a\hat i+6\hat j-8\hat k)\) are collinear. |
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