Ex 10.2, 14 - Class 12

Transcript

Ex 10.2, 14 Show that the vector 𝑖﷯ + 𝑗﷯ + 𝑘﷯ is equally inclined to the axes OX, OY and OZ. Let 𝑎﷯ = 𝑖﷯ + 𝑗﷯ + 𝑘﷯ = 1 𝑖﷯ + 1 𝑗﷯ + 1 𝑘﷯ A vector is equally inclined to OX, OY, OZ i.e. X, Y and Z axes respectively, if its direction cosines are equal. Direction ratios of 𝑎﷯ are 𝑎 = 1, b = 1 , c = 1 Magnitude of 𝑎﷯ = ﷮12+12+12﷯ 𝑎﷯﷯ = ﷮1+1+1﷯ = ﷮3﷯ Direction cosines OF 𝑎﷯ are 𝑎﷮ 𝑎﷯﷯﷯, 𝑏﷮ 𝑎﷯﷯﷯, 𝑐﷮ 𝑎﷯﷯﷯﷯ = 1﷮ ﷮3﷯﷯, 1﷮ ﷮3﷯﷯, 1﷮ ﷮3﷯﷯﷯ Since the direction cosines are equal, 𝑎﷯ = 𝑖﷯ + 𝑗﷯ + 𝑘﷯ is equally inclined to OX, OY and OZ