Physics - Grade XI or Standard XI
Resultant Vector by Calculation
Resultant vector:
Given the two vectors P and Q, we can find their resultant by calculation as follows:
Let P = Px i + Py j + Pz k
Let Q = Qx i + Qy j + Qz k
Here, Px, Py, and Pz are x, y, and z components of vector P and Qx, Qy, and Qz are x, y, and z components of vector Q. Let vector R be the resultant of vectors P and Q. Then we have:
P = P + Q
P = (Px i + Py j + Pz k) + (Qx i + Qy j + Qz k)
R = (Px + Qx) i + (Py + Qy) j + (Pz + Qz) k
R = Rx i + Ry j + Rz k
where Rx, Ry, and Rz are x, y, and z components of resultant vector R and their values are given by:
Rx = Px + Qx
Ry = Py + Qy
Rz = Pz + Qz
Example of resultant vector by calculation:
Find the resultant vector of vectors A and B such that:
A = 9 i - 10 j + 8 k
B = -7 i + 3 j + 4 k
Here, we have: Ax = 9, Ay = -10, Az = 8, Bx = -7, By = 3, Bz = 4. Let vector C be the resultant of vectors A and B. Then we have:
C = (Ax + Bx) i + (Ay + By) j + (Az + Bz) k
C = (9 + (-7) i + (-10 + 3) j + (8 + 4) k
C = 2 i -7 j + 12 k -----------------------------(Answer)
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