Question 262 of 379MediumNUMERICAL
Let a,b,c satisfy ∣a∣=2, ∣b∣=4, ∣c∣=4. If the projection of b on a equals the projection of c on a, and b⊥c, then ∣a+b−c∣ is \_\_\_\_\_\_\_.
Answer: 6 Solutions · 1
Official solution
Equal projections: a⋅b=a⋅c. Given b⋅c=0.
\[|\vec a+\vec b-\vec c|^2 = |\vec a|^2+|\vec b|^2+|\vec c|^2+2\vec a\cdot\vec b-2\vec a\cdot\vec c-2\vec b\cdot\vec c = 4+16+16+0-0-0=36\]
\[|\vec a+\vec b-\vec c|=6\] Answer the question to unlock