A man start from a point A and walk a distance of 8.0 km due northeast to point B from B he then walks 4.0 km due South East to point x. Calculate the shortest distance between A and x.
AX⃗=AB⃗+BX⃗\vec{AX}=\vec{AB}+\vec{BX}AX=AB+BX
∠(AB⃗,BX⃗)=∠(NE⃗,SE⃗)=π2\angle(\vec{AB},\vec{BX})=\angle(\vec{NE},\vec{SE})=\frac{\pi}{2}∠(AB,BX)=∠(NE,SE)=2π
AX⃗2=(AB⃗+BX⃗)2\vec{AX}^2=(\vec{AB}+\vec{BX})^2AX2=(AB+BX)2
AX⃗2=AB⃗2+BX⃗2+2AB⃗∗BX⃗\vec{AX}^2=\vec{AB}^2+\vec{BX}^2+2\vec{AB}*\vec{BX}AX2=AB2+BX2+2AB∗BX
2AB⃗∗BX⃗=2∗AB∗BX∗cos(∠(AB⃗,BX⃗))=02\vec{AB}*\vec{BX}=2* AB*BX*\cos(\angle(\vec{AB},\vec{BX}))=02AB∗BX=2∗AB∗BX∗cos(∠(AB,BX))=0
AX2=AB2+BX2AX^2 =AB^2+BX^2AX2=AB2+BX2
AX=AB2+BX2=82+42=8.94AX =\sqrt{AB^2+BX^2}=\sqrt{8^2+4^2}=8.94AX=AB2+BX2=82+42=8.94
Answer : AX=8.94 km\text{Answer : }AX =8.94\ kmAnswer : AX=8.94 km
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