vector A has a magnitude of 29 units when B is added to A . find magnitude of B.
To find the magnitude of vector B when vector A has a magnitude of 29 units, you can use the concept of vector addition and subtraction.
1. Start by representing vector A with its magnitude and direction. Let's assume that vector A is represented by a line segment from the origin to point P.
- |A| = 29 units
2. Now, represent vector B by drawing a line segment with its starting point at point P and extending in the direction of vector B.
3. To find the magnitude of vector B, we need to find the length of the line segment representing vector B. We can do this by using the properties of vector addition.
4. Add vector B to vector A by placing the tail of vector B at point P, the endpoint of vector A. The resulting vector is the sum of A and B, represented by a line segment from the origin to the endpoint of vector B.
5. The magnitude of the resulting vector (A + B) is given as 29 units. Let's denote the magnitude of vector B as |B|.
6. Now, you have a triangle formed by vector A, vector B, and the resulting vector (A + B). Since you know the magnitude of vector A and the magnitude of the resulting vector, you can use the triangle inequality to solve for |B|.
- |A + B| ≤ |A| + |B|
- |A + B| ≤ 29 + |B|
Since |A + B| = 29 units, the inequality becomes:
29 ≤ 29 + |B|
Subtracting 29 from both sides:
29 - 29 ≤ |B|
0 ≤ |B|
So, the magnitude of vector B is zero units.
Therefore, the magnitude of vector B is 0 units when vector A has a magnitude of 29 units.