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Find a unit vector in the direction of vec(a)=2 hat(ı)+3 hat(ȷ)+ hat(k).

11. Find a unit vector in the direction of a⃗=2ı^+3ȷ^+k^ \vec{a}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k} .

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Full solution

Q. 11. Find a unit vector in the direction of a⃗=2ı^+3ȷ^+k^ \vec{a}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k} .
  1. Calculate Magnitude: Calculate the magnitude of a⃗\vec{a}.Magnitude=(2)2+(3)2+(1)2=4+9+1=14\text{Magnitude} = \sqrt{(2)^2 + (3)^2 + (1)^2} = \sqrt{4 + 9 + 1} = \sqrt{14}
  2. Find Unit Vector: Find the unit vector by dividing each component of a⃗\vec{a} by its magnitude.\newlineUnit vector = 214\frac{2}{\sqrt{14}} ı^\hat{\imath} + 314\frac{3}{\sqrt{14}} ȷ^\hat{\jmath} + 114\frac{1}{\sqrt{14}} k^\hat{k}

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