The number of unit vectors of the form a hat{ | vedclass

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(C) vector $\vec{v} = a \hat{i} + b \hat{j} + c \hat{k}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{v}| = \sqrt{a^2 + b^2 + c^2} = 1$.Squari

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$3$

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(C) vector $\vec{v} = a \hat{i} + b \hat{j} + c \hat{k}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{v}| = \sqrt{a^2 + b^2 + c^2} = 1$.Squaring both sides,we get $a^2 + b^2 + c^2 = 1$.Given that $a, b, c \in W$,where $W = \{0, 1, 2, 3, \dots\}$ is the set of whole numbers.Since $a^2, b^2, c^2 \ge 0$,the only way for their sum to be $1$ is if one of the variables is $1$ and the others are $0$.The possible triplets $(a, b, c)$ are $(1, 0, 0)$,$(0, 1, 0)$,and $(0, 0, 1)$.Thus,there are $3$ such unit vectors.

The number of unit vectors of the form $a \hat{i} + b \hat{j} + c \hat{k}$,where $a, b, c \in W$ is

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