Ex 10.2, 16

Transcript

Ex 10.2, 16 Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2). P(2,3,4) , Q(4, 1, −2) Let the midpoint of PQ be R. Position vector of P = (2 − 0) 𝑖﷯ + (3 − 0) 𝑗﷯ + (4 − 0) 𝑘﷯ 𝑂𝑃﷯ = 2 𝑖﷯ + 3 𝑗﷯ + 4 𝑘﷯ Position vector of Q = (4 − 0) 𝑖﷯ + (1 − 0) 𝑗﷯ + (−2 − 0) 𝑘﷯ 𝑂𝑄﷯ = 4 𝑖﷯ + 1 𝑗﷯ − 2 𝑘﷯ Position vector of R = 𝑶𝑸﷯ + 𝑶𝑷﷯﷮𝟐﷯ 𝑂𝑅﷯ = 4 𝑖﷯ + 1 𝑗﷯ − 2 𝑘﷯﷯ + (2 𝑖﷯ + 3 𝑗﷯ + 4 𝑘﷯)﷮2﷯ 𝑂𝑅﷯ = 4 + 2﷯ 𝑖﷯ + 1 + 3﷯ 𝑗﷯ + (−2 + 4) 𝑘﷯﷮2﷯ 𝑂𝑅﷯ = 6 𝑖﷯ + 4 𝑗﷯ + 2 𝑘﷯﷮2﷯ 𝑂𝑅﷯ = 2(3 𝑖﷯ + 2 𝑗﷯ + 𝑘﷯)﷮2﷯ 𝑂𝑅﷯ = 𝟑 𝒊﷯+𝟐 𝒋﷯+ 𝒌﷯ Therefore, position vector of midpoint of PQ is 3 𝑖﷯ + 2 𝑗﷯ + 𝑘﷯