Final answer:
The expressions involve performing vector addition and scalar multiplication to find the resultant vectors. For |u + 3v|, the result is √373. For 4u + 2v, the vector is (26, 8, 18√2), and for 2u - v, it's (11, 4, 3√2).
Step-by-step explanation:
To evaluate expressions with vectors, you will perform vector addition and scalar multiplication.
a. |u + 3v|
To find the magnitude of the vector u + 3v, first perform the vector addition and multiplication:
u + 3v = (6,2,3√2) + 3(1,0,3√2) = (6+3, 2+0, 3√2+9√2) = (9, 2, 12√2)
Now find the magnitude of the resulting vector:
|u + 3v| = √(9^2 + 2^2 + (12√2)^2) = √(81 + 4 + 288) = √373
b. 4u + 2v
The vector 4u + 2v is calculated by:
4u + 2v = 4(6,2,3√2) + 2(1,0,3√2) = (24,8,12√2) + (2,0,6√2) = (26, 8, 18√2)
c. 2u - v
Lastly, for the vector 2u - v:
2u - v = 2(6,2,3√2) - (1,0,3√2) = (12,4,6√2) - (1,0,3√2) = (11, 4, 3√2)