CBSE-XI-Physics
02: Physics and Mathematics
- #4Let
a→=4i→+3j→andb→=3i→+4j→. (a) Find the magnitudes of (a)
a→, (b)
b→, (c)
a→+b→and(d)
a→-b→.digAnsr: ivAns : Given: `` \stackrel{\to }{a}=4\stackrel{\to }{i}+3\stackrel{\to }{j}\mathrm{and}\stackrel{\to }{b}=3\stackrel{\to }{i}+4\stackrel{\to }{j}``
(a) Magnitude of `` \stackrel{\to }{a}`` is given by `` \left|\stackrel{\to }{a}\right|=\sqrt{{4}^{2}+{3}^{2}}=\sqrt{16+9}=5``
(b) Magnitude of `` \stackrel{\to }{b}`` is given by `` \left|\stackrel{\to }{b}\right|=\sqrt{{3}^{2}+{4}^{2}}=\sqrt{9+16}=5``
(c) `` \stackrel{\to }{a}+\stackrel{\to }{b}=(4\vec{i}+3\vec{j})+(3\vec{i}+4\vec{j})=(7\vec{i}+7\vec{j})``
∴ Magnitude of vector `` \stackrel{\to }{a}+\stackrel{\to }{b}`` is given by `` \left|\stackrel{\to }{a}+\stackrel{\to }{b}\right|=\sqrt{49+49}=\sqrt{98}=7\sqrt{2}``
(d) `` \stackrel{\to }{a}-\stackrel{\to }{b}=\left(4\stackrel{\to }{i}+3\stackrel{\to }{j}\right)-\left(3\stackrel{\to }{i}+4\stackrel{\to }{j}\right)=\stackrel{\to }{i}-\stackrel{\to }{j}``
∴ Magnitude of vector `` \stackrel{\to }{a}-\stackrel{\to }{b}`` is given by `` \left|\stackrel{\to }{a}-\stackrel{\to }{b}\right|=\sqrt{{\left(1\right)}^{2}+{\left(-1\right)}^{2}}=\sqrt{2}``
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