vector a has a negative x component 3 units in length and positive y component 2 units in length. What vector B when added to vector A gives a resultant vector with no x component and a negative y component 4 units in length
A+B=-4j
-3i+2j+B=-4j
B=3i-6j
To find vector B, we need to balance the x and y components of the resultant vector by canceling out the x component and adding a negative y component of 4 units.
Given:
Vector A = (-3, 2)
Resultant vector = (0, -4)
Let's assume vector B = (x, y).
To balance the x component, x + (-3) = 0
Solving for x:
x - 3 = 0
x = 3
To balance the y component, y + 2 + (-4) = 0
Solving for y:
y - 2 - 4 = 0
y - 6 = 0
y = 6
Therefore, vector B is (3, 6).
To find vector B that, when added to vector A, gives a resultant vector with certain properties, we need to break down the problem into its components and equations.
Let's break down vector A:
- x component: negative 3 units
- y component: positive 2 units
The resultant vector has no x component and a negative y component of 4 units. Let's denote the components of vector B as follows:
- x component: Bx
- y component: By
Now, we can set up the equations based on the component requirements:
Equation 1: x component equation
A_x + B_x = 0
(-3) + B_x = 0
B_x = 3
Equation 2: y component equation
A_y + B_y = -4
2 + B_y = -4
B_y = -6
So, vector B has a x component of 3 and a y component of -6.
Therefore, vector B is B = (3, -6).