0.4hat i + 0.8hat j + chat k represents a uni | vedclass

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(B) vector $\vec{A} = a_x\hat{i} + a_y\hat{j} + a_z\hat{k}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{A}| = \sqrt{a_x^2 + a_y^2 + a_z^2} =

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$\sqrt{0.2}$

Vedclass · Answer

(B) vector $\vec{A} = a_x\hat{i} + a_y\hat{j} + a_z\hat{k}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{A}| = \sqrt{a_x^2 + a_y^2 + a_z^2} = 1$.Given vector is $\vec{A} = 0.4\hat{i} + 0.8\hat{j} + c\hat{k}$.Calculating the magnitude: $\sqrt{(0.4)^2 + (0.8)^2 + c^2} = 1$.Squaring both sides: $(0.4)^2 + (0.8)^2 + c^2 = 1^2$.$0.16 + 0.64 + c^2 = 1$.$0.80 + c^2 = 1$.$c^2 = 1 - 0.80 = 0.20$.Therefore,$c = \sqrt{0.2}$.

$0.4\hat i + 0.8\hat j + c\hat k$ represents a unit vector when $c$ is

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