Given that a = 5i +2j - k and b = I - 3j + k. Find (a + b) x (a + b).
a+b = 6 i -1 j + 0 k
trick question or typo
cross product = |A||A| sin theta
theta = 0
so cross product = 0
correct. You didn't even have to find a+b.
Given that a = 5i +2j - k and b = I - 3j + k. Find (a + b) x (a + b).
To find the cross product of two vectors, we need to use the determinant method. Let's first find the sum of vectors a and b.
Given that a = 5i + 2j - k and b = i - 3j + k, we can find a + b as follows:
a + b = (5i + 2j - k) + (i - 3j + k)
= 5i + 2j - k + i - 3j + k
= (5i + i) + (2j - 3j) + (-k + k)
= 6i - j
So, a + b = 6i - j.
Now, let's find the cross product of a + b with itself, (a + b) x (a + b):
The cross product, denoted by ×, is defined as follows:
(a + b) x (a + b) = | i j k |
| 6 -1 0 |
| 0 0 0 |
To find the cross product, we calculate the determinant of the 3x3 matrix formed by the i, j, and k components of the vectors.
The determinant can be calculated as follows:
(a + b) x (a + b) = (6 * 0 * 0) + (-1 * 0 * 0) + (0 * 0 * 0) - (0 * (-1) * 0) - (6 * 0 * 0) - (0 * 0 * 0)
= 0 + 0 + 0 - 0 - 0 - 0
= 0
Therefore, (a + b) x (a + b) = 0.