Question

Find the magnitude of the vector sum r of the vector displacements c and d whose components in meters along three perpendicular directions are c_x= 7.3, c_y= -3.8, c_z= -6.5; d_x= 4.5, d_y= -2.3, d_z= 3.3;

Answer 1

Given that for vector C

cx= 7.3, cy= -3.8, cz= -6.5

C = 7.3 i - 3.8 j - 6.5 k

Given that for vector D

dx= 4.5, dy= -2.3, dz= 3.3

D = 4.5 i - 2.3 j + 3.3 k

So vector sum of C and D will be

r = C + D

r = (7.3 i - 3.8 j - 6.5 k) + (4.5 i - 2.3 j + 3.3 k)

r = (7.3 + 4.5) i + (-3.8 - 2.3) j + (-6.5 + 3.3) k

r = 11.8 i - 6.1 j -3.2 k

Now magnitude of r will be

if r = rx i + ry j + rz k, then

|r| = sqrt (rx^2 + ry^2 + rz^2)

|r| = sqrt (11.8^2 + (-6.1)^2 + (-3.2)^2)

|r| = 13.66

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