three force vector a,b,c are acting at apoint A= 4i -3j and B =2i+j and A+B-C= 0 find a unit vector c.

Answer 1

To find vector C, we need to solve the equation A + B - C = 0. Let's substitute the given values of vector A and vector B into the equation:

4i - 3j + 2i + j - C = 0

Combining like terms:

(4i + 2i) + (-3j + j) - C = 0
6i - 2j - C = 0

Now, we can rearrange the equation to solve for vector C:

C = 6i - 2j

To find the unit vector of C, we need to divide vector C by its magnitude. The magnitude of a vector given by the components a and b is sqrt(a^2 + b^2). Let's calculate the magnitude of vector C:

|C| = sqrt((6)^2 + (-2)^2)
= sqrt(36 + 4)
= sqrt(40)
= 2sqrt(10)

Now, to find the unit vector, we divide vector C by its magnitude:

Unit vector of C = C/|C|
= (6i - 2j) / (2sqrt(10))
= (3/sqrt(10))i - (1/sqrt(10))j

Therefore, the unit vector of C is (3/sqrt(10))i - (1/sqrt(10))j.