if the displacement vector in m are given as A 12i+25j+13k and B 3i+7k t find the resultant vector and it direction A is subtracted from B

Answer 1

To find the resultant vector when A is subtracted from B, we need to subtract the components of vector A from vector B.

Vector A = 12i + 25j + 13k
Vector B = 3i + 0j + 7k (since there is no component for j in vector B)

To subtract vector A from vector B, we need to subtract the corresponding components:

B - A = (3 - 12)i + (0 - 25)j + (7 - 13)k
= -9i - 25j - 6k

Therefore, the resultant vector when vector A is subtracted from vector B is:

Resultant vector = -9i - 25j - 6k

To find the direction of the resultant vector, we can calculate the magnitude of the resultant vector using:

Magnitude = sqrt((-9)^2 + (-25)^2 + (-6)^2) = sqrt(81 + 625 + 36) = sqrt(742) ≈ 27.23

And the direction can be given by the unit vector in the direction of the resultant vector:

Unit vector = (-9i - 25j - 6k) / 27.23
= (-9/27.23)i + (-25/27.23)j + (-6/27.23)k
≈ -0.33i - 0.92j - 0.22k

Therefore, the resultant vector when vector A is subtracted from vector B is approximately -27.23 units in the direction of -0.33i - 0.92j - 0.22k.