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

Given, vector a=î+ĵ+k̂. Comparing with a=xî+yĵ+zk̂ We get x=1, y=1, z=1. The magnitude of given vector is |a|=î+ĵ+k̂=√(x^2+y^2+z^2)=√(1^2+1^2+1^2)=√(3) Simil ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Compute the m...

Question

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

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Solution

Given, vector $a =^i +^j +^k$ . Comparing with $a = x^i + y^j + z^k$
We get $x = 1, y = 1, z = 1.$
The magnitude of given vector is
$| a | =^i +^j +^k = \sqrt{x^{2} + y^{2} + z^{2}} = \sqrt{1^{2} + 1^{2} + 1^{2}} = \sqrt{3}$
Similarly magnitude of $b = | b | = | 2^i - 7^j - 3^k | = \sqrt{2^{2} + (- 7)^{2} + (- 3)^{2}}$
= $\sqrt{4 + 49 + 9} = \sqrt{62}$
$a n d | c | = ∣ ∣ \begin{matrix} \frac{1}{\sqrt{3}}^i + \frac{1}{\sqrt{3}}^j - \frac{1}{\sqrt{3}}^k \end{matrix} ∣ ∣$
= $\sqrt{{(\frac{1}{\sqrt{3}})}^{2} + {(\frac{1}{\sqrt{3}})}^{2} + {(- \frac{1}{\sqrt{3}})}^{2}} = \sqrt{\frac{1}{3} + \frac{1}{3} + \frac{1}{3}} = 1$

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Similar questions

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

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Let $\to a =^i +^j +^k, \to b =^i -^j +^k$ and $\to c =^i -^j -^k$ be three vectors. A vector $\to v$ in the plane of
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Compute the magnitude of the following vectors: a=^i+^j+^k;b=2^i−7^j−3^k;c=1√3^i+1√3^j−1√3^k.

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