# Find the dot product of P=4,82i-2,33j+5,47k N and Q=-2,81i-6,09j+1,12k N

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The dot product of two forces is given as the sum of the products of their x , y and z components.

Here we have:

P = 4.82i - 2.33j + 5.47 kN

and Q = -2.81i - 6.09j + 1.12 kN

Now the product of the x components is:

= (4.82)(-2.81) = -13.5442

The product of the y components is:

= (-2.33)(-6.09) = 14.1897

The product of the z components is

= (5.47)(1.12) = 6.1264

Now to get P dot Q add the three:

=> -13.5442 + 14.1897 + 6.1264 = 6.7619

**Therefore the required dot product of P and Q is 6.7619**

The dot product of P and Q is:

P*Q = Px*Qx + Py*Qy + Pz*Qz

The products Px*Qx, Py*Qy and Pz*Qz are the products of the coefficients of the unit vectors.

Px*Qx = (4.82)(-2.81)

Px*Qx = -13.5442

Py*Qy = (-2.33)(-6.09)

Py*Qy = 14.1897

Pz*Qz = (5.47)(1.12)

Pz*Qz = 6.1264

Now, we'll substitute the results in the expression of dot product:

P*Q = -13.5442 + 14.1897 + 6.1264

**The dot product of P and Q is:**

**P*Q = 6.7719**