Question

Three of vectors A,B and C are acting point if A=4i-3j,B 2i+j and c= A+B-C=0.find a, the magnitude and direction of vector C and b,a unit vector along C

Answer 1

To find the magnitude and direction of vector C, we can use the fact that A + B - C = 0. Rearranging the equation, we have C = A + B. The magnitude of vector C is sqrt(40) and its direction is -18.43 degrees or 341.57 degrees. A unit vector along C is 0.9487i - 0.3162j.

Step-by-step explanation:

To find the magnitude and direction of vector C, we can use the fact that A + B - C = 0.

Rearranging the equation, we have C = A + B.

Substituting the given values, we get

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

= 6i - 2j.

The magnitude of vector C is

|C| = sqrt((6^2) + (-2^2))

= sqrt(40).

The direction of vector C can be found by calculating the tangent of the angle it makes with the positive x-axis: tan(theta) = (-2) / 6.

Therefore, the angle is

theta = arctan((-2) / 6)

= -18.43 degrees or 341.57 degrees.

To find a unit vector along C, we divide vector C by its magnitude:

C_unit = C / |C|

= (6i - 2j) / sqrt(40)

= 0.9487i - 0.3162j.