Q.226. Vectors.

Question 226.
Point B divides circle arc AC = 90 (degrees) with ratio 1:2. O - is the center of the circle. Express vector OC = c with vectors OA = a and OB = b.

Answer 226.
Let l OA l = l OB l = l OC l = r
=>
OA = r i
OB = rcos30° i + rsin30° j = r (√3/2 i + j/2)
OC = r j

Let OC = mOA + nOB
=> r j = m * r i + n * r (√3/2 i + j/2)
=> m + (√3/2)n = 0 and 1 = n/2
=> n = 2 and m = - √3

=> OC = - √3 OA + 2 OB
=> OC = - √3a + 2b.

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