If r-r-r-k- and -r-3- then find r-A- - 3-k-B- -1-3-k-C- -1-3-k-D- -3-k-

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Multiplication with Vectors

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Question

If $\to r .^i = \to r .^j = \to r .^k$ and $| r | = 3$ , then find $\to r$ .

\pm 3 (^i +^j +^k)

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\pm \frac{1}{3} (^i +^j +^k)

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\pm \frac{1}{\sqrt{3}} (^i +^j +^k)

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\pm \sqrt{3} (^i +^j +^k)

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Solution

The correct option is D $\pm \sqrt{3} (^i +^j +^k)$
Let $r = x^i + y^j + z^k$ .

Scalar product of a vector with a unit vector of x, y and z axis gives us the magnitude of vector in x, y and z direction i.e. the value of x, y and z.

Since, $\to r .^i = \to r .^j = \to r .^k \Rightarrow x = y = z \dots \dots (i)$
Also,
$| r | = 3 = \sqrt{x^{2} + y^{2} + z^{2}} = \sqrt{x^{2} + x^{2} + x^{2}} \sqrt{3 x^{2}} = 3 \sqrt{3} x = 3 x = \pm \sqrt{3}$

Hence the required vector,
$\to r = \pm \sqrt{3} (^i +^j +^k)$

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If →r.^i=→r.^j=→r.^k and |r|=3, then find →r.

If $\to r .^i = \to r .^j = \to r .^k$ and $| r | = 3$ , then find $\to r$ .