Find the coordinates of the vector a (2t; -t; t) if its length √54
| August 9, 2021 | education
a (2t; -t; t).
The length of the vector is calculated by the formula: | a | = √ (x ^ 2 + y ^ 2 + z ^ 2).
| a | = √ ((2t) ^ 2 + (-t) ^ 2 + t ^ 2) = √ (4t ^ 2 + t ^ 2 + t ^ 2) = √ (6t ^ 2).
By assumption, the length of the vector is √54.
Therefore, √ (6t ^ 2) = √54.
6t ^ 2 = 54.
t ^ 2 = 54/6.
t ^ 2 = 9.
t1 = 3 or t2 = -3.
Substitute the obtained values of t into the condition and get:
t1 = 3 – vector a (6; -3; 3).
t2 = -3 – vector a (-6; 3; -3).
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