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Question:
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Consider the following inequalities in respect of vectors
$\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}:$
$1.$ $\quad|\vec{a}+\vec{b}|_{£}|\vec{a}|+|\vec{b}|$
$2.$ $\quad|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|^{3}|\overrightarrow{\mathrm{a}}|-|\overrightarrow{\mathrm{b}}|$
Which of the above is/are correct?
Options:
$\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}:$
$1.$ $\quad|\vec{a}+\vec{b}|_{£}|\vec{a}|+|\vec{b}|$
$2.$ $\quad|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|^{3}|\overrightarrow{\mathrm{a}}|-|\overrightarrow{\mathrm{b}}|$
Which of the above is/are correct?
Solution:
2895 Upvotes
Verified Answer
The correct answer is:
Both 1 and 2
$\begin{aligned} \text { } &|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}| \leq|\overrightarrow{\mathrm{a}}|+|\overrightarrow{\mathrm{b}}| \\ &|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}| \geq|\overrightarrow{\mathrm{a}}|-|\overrightarrow{\mathrm{b}}| \end{aligned}$
both are correct.
both are correct.
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