Question

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If OA = 3i + 2j – 4k and OB = 4i + 5j – 2k, P divides AB in the ratio 3:-2. Determine the modulus of OP leaving your answer to 1 decimal place. Given that O is the origin.

Answer 1

Let p be point (x, y, z)
          x             3         4
1/3   y + 2/3      2      = 5
          Z            -4        -2

P(6,11,2)
10p1 = √ (6)2 + (11)2 + (2)2
= √ 161 = 12.69 units