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Maths-

General

Easy

Question

If $r. i equals r. j equals r. k$ and $vertical line r vertical line equals 3 comma$ then $r equals$

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

The correct answer is: $plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis$

Let $r equals x i plus y j plus z k.$ Since $r. i equals r. j equals r. k$
$rightwards double arrow x equals y equals z$ .....(i)
Also $vertical line r vertical line equals square root of x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent end root equals 3 rightwards double arrow x equals plus-or-minus square root of 3$ , {By (i)}
Hence the required vector $r equals plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis.$
Trick : As the vector $plus-or-minus square root of 3 left parenthesis i plus j plus k right parenthesis$ satisfies both the conditions.

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Physics-General

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