If |vec"a"| = 4 and −3 $\leq$ λ $\leq$ 2, then the range of |lambdavec"a"| is ______.

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If |vec"a"| = 4 and −3 $\leq$ λ $\leq$ 2, then the range of |lambdavec"a"| is [–12, 8]. Explanation: Given that |vec"a"| = 4, −3 $\leq$ λ $\leq$ 2 Now `|lambdavec"a"| = lambda|vec"a"| = lambda * 4 = 4lambda Here −3 $\leq$ λ $\leq$ 2 $\Rightarrow$ -3.4 $\leq$ 4lambda $\leq$ 2.4 $\Rightarrow$ -12 $\leq$ 4lambda $\leq$ 8 $\therefore$ 4lambda` = [–12, 8]

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