Compute the magnitude of the following vectors- a-k- b-2-7-3k- c-1-3-1-3-1-3k-

The given vectors are: a⃗=î+ĵ+k̂; #10;b=2î 7ĵ 3k̂; c⃗=1√(3)#10;i+1√(3)ĵ 1√(3)k̂ Magnitude of these vectors are given by, |a⃗ |=√((1)^2+(1)^2+(1)^2)=√(3) ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

Compute the m...

Question

Compute the magnitude of the following vectors:
$\to a =^i +^j +^k; \to b = 2^i - 7^j - 3^k; \to c = \frac{1}{\sqrt{3}}^i + \frac{1}{\sqrt{3}}^j - \frac{1}{\sqrt{3}}^k$

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Solution

The given vectors are:
$\to a =^i +^j +^k; \to b = 2^i - 7^j - 3^k; \to c = \frac{1}{\sqrt{3}}^i + \frac{1}{\sqrt{3}}^j - \frac{1}{\sqrt{3}}^k$
Magnitude of these vectors are given by,
$| \to a | = \sqrt{(1)^{2} + (1)^{2} + (1)^{2}} = \sqrt{3}$
$∣ ∣ \to b ∣ ∣ = \sqrt{(2)^{2} + (- 7)^{2} + (- 3)^{2}}$
$= \sqrt{4 + 49 + 9} = \sqrt{62}$
$| \to c | = \sqrt{{(\frac{1}{\sqrt{3}})}^{2} + {(\frac{1}{\sqrt{3}})}^{2} + {(- \frac{1}{\sqrt{3}})}^{2}}$
$= \sqrt{\frac{1}{3} + \frac{1}{3} + \frac{1}{3}} = 1$

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