Vectors u=2i+9j+0k and v=13i+18j+0k. What is the value of |u×v|?
This is the magnitude of the cross product.
The cross product is obtained by evaluating the determinant
p
i j k
2 9 0
13 18 0
which is
p=0i+0j+(2*18-9*13)k
=-81k
The magnitude is therefore 81.
thanks sir!!!!
You're welcome!
To find the value of the cross product magnitude |u×v|, we first need to calculate the cross product u×v.
The cross product of two 3-dimensional vectors u = u₁i + u₂j + u₃k and v = v₁i + v₂j + v₃k is given by the formula:
u × v = (u₂v₃ - u₃v₂)i + (u₃v₁ - u₁v₃)j + (u₁v₂ - u₂v₁)k
In this case, u = 2i + 9j + 0k and v = 13i + 18j + 0k. Let's calculate the cross product:
u × v = (2 * 18 - 9 * 13)i + (9 * 13 - 2 * 18)j + (2 * 18 - 9 * 13)k
= (36 - 117)i + (117 - 36)j + (36 - 117)k
= -81i + 81j - 81k
Now, we need to find the magnitude |u × v| of the obtained vector (-81i + 81j - 81k).
The magnitude or length of a 3-dimensional vector a = ai + bj + ck is given by the formula:
|a| = √(a₁² + a₂² + a₃²)
In this case, |u × v| = √((-81)² + 81² + (-81)²)
= √(6561 + 6561 + 6561)
= √(3 * 6561)
= √(19683)
= 139.98
Therefore, the value of |u × v| is approximately 139.98.