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Vector Algebra

Question
CBSEENMA12033942
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If open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 3 space and space space minus space 4 space less or equal than space straight k space less or equal than space 1 comma then what can you say about open vertical bar straight k space straight a with rightwards arrow on top close vertical bar ?

Solution

Here,             open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 3 comma space space space space minus space 4 space less or equal than space straight k space less or equal than space 1
           When            k = -4,   open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k close vertical bar space open vertical bar straight a with rightwards arrow on top close vertical bar space equals negative open vertical bar negative 4 space left enclose left parenthesis 3 end enclose right parenthesis close vertical bar space equals space 4 space cross times space 3 space equals space 12
            When            k = 1,   open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k close vertical bar space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space left parenthesis 1 right parenthesis thin space left parenthesis 3 right parenthesis space equals space 3
           Also,  
                    open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space space greater or equal than space 0 therefore space space space space space space 0 space less or equal than space open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space less or equal than space 12.

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