The concept i get, but somehow i just can't execute this problem, please help me!
You are given vectors A = 5.5 6.2 and B = - 3.7 7.4 . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 19.0.
I need x and y components for vector C
A = 5.5 i + 6.2 j
B = -3.7i + 7.4 j
C = x i + y j
A dot C = |A| |C| cos theta
if perpendicular theta is 90 degrees and cos theta = 0
so
5.5 x + 6.2 y = 0
B dot C = 19
so
-3.7 x + 7.4 y = 19.0
solve those two equations for x and y
5.5(_3.7x+7.4y=19)
3.7(5.5X+2.2y=0)
(20.35x+22.94y=0)
+ (_20.35x+40.70y=384.65)
Y=384.68/63.64
X=_(22.94(384.68/63.64)/20.35)
To find the x and y components of vector C, we first need to determine the z component because C lies in the xy-plane (meaning it has no z component).
Since vector C is perpendicular to vector A, we know that the dot product of C and A is zero.
The dot product of two vectors is given by:
A · C = Ax * Cx + Ay * Cy + Az * Cz
Since we want to find the x and y components of C, we can simplify the equation as follows:
0 = A * C = Ax * Cx + Ay * Cy
Given that A = 5.5 6.2 and C = Cx Cy, we can substitute these values into the equation:
0 = (5.5 * Cx) + (6.2 * Cy)
Next, we use the information that the scalar product (dot product) of C with B is 19.0:
B · C = Bx * Cx + By * Cy + Bz * Cz
Since C lies in the xy-plane, the z component of C is zero, so the equation simplifies to:
19.0 = B * C = Bx * Cx + By * Cy
Given that B = -3.7 7.4 and C = Cx Cy, we can substitute these values into the equation:
19.0 = (-3.7 * Cx) + (7.4 * Cy)
Now we have a system of two equations:
0 = 5.5 * Cx + 6.2 * Cy
19.0 = -3.7 * Cx + 7.4 * Cy
To solve this system of equations, we can use a variety of methods such as substitution or elimination. Solving the system will give us the values for Cx and Cy, which are the x and y components of vector C.