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Applications of Dot Product

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Question

If $^a,^b$ and $^c$ are mutually perpendicular unit vectors, then find the value of $| 2^a +^b +^c |$ .

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Solution

$| 2^a +^b +^c |$ represents the distance between the points $(0, 0, 0)$ and $(2, 1, 1)$ in the $(^a,^b,^c)$ space.
Thus, by distance formula, we have
$| 2^a +^b +^c | = \sqrt{2^{2} + 1^{2} + 1^{2}} = \sqrt{6} .$

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^a,^b,^c

are mutually perpendicular unit vectors, then

∣ ∣^a +^b +^c ∣ ∣

Q. Arrange the value of

| a + b + c |

in ascending order

A

^a,^b,^c

are mutually perpendicular unit vectors

B

^a,^b,^c

are vectors of lengths 2,3,4 respectively and

^a,^b,^c

are perpendicular to

^b +^c,^c +^a,^a +^b

C

^a,^b,^c

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^a,^b,^c

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\to b

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^c

^a

^b

^c

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| 2^a + 5^b + 5^c |

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