Ex 10.2, 8

Transcript

Ex 10.2, 8 Find the unit vector in the direction of vector 𝑃𝑄﷯ , where P and Q are the points (1, 2, 3) and (4, 5, 6); respectively. P (1, 2, 3) Q (4, 5, 6) 𝑃𝑄﷯ = (4 – 1) 𝑖﷯ + (5 – 2) 𝑗﷯ + (6 – 3) 𝑘﷯ = 3 𝑖﷯ + 3 𝑗﷯ + 3 𝑘﷯ ∴ Vector joining P and Q is given by 𝑃𝑄﷯ = 3 𝑖﷯ + 3 𝑗﷯ + 3 𝑘﷯ Magnitude of 𝑃𝑄﷯ = ﷮32+32+32﷯ 𝑃𝑄﷯﷯ = ﷮9+9+9﷯ = ﷮27﷯ = 3 ﷮3﷯ Unit vector in direction of 𝑃𝑄﷯ = 1﷮𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑃𝑄﷯﷯× 𝑃𝑄﷯ = 1﷮3 ﷮3﷯﷯ 3 i﷯ + 3 j﷯ + 3 k﷯﷯ = 3﷮3 ﷮3﷯﷯ 𝑖﷯ + 3﷮3 ﷮3﷯﷯ 𝑗﷯ + 3﷮3 ﷮3﷯﷯ 𝑘﷯ = 𝟏﷮ ﷮𝟑﷯﷯ 𝒊﷯ + 𝟏﷮ ﷮𝟑﷯﷯ 𝒋﷯ + 𝟏﷮ ﷮𝟑﷯﷯ 𝒌﷯ Thus, unit vector in direction of 𝑃𝑄﷯ = 1﷮ ﷮3﷯﷯ 𝑖﷯ + 1﷮ ﷮3﷯﷯ 𝑗﷯ + 1﷮ ﷮3﷯﷯ 𝑘﷯