Final answer:
The magnitude or length of the vector a <−1, −4, 3> can be found using the formula: |a| = sqrt(a1^2 + a2^2 + a3^2). Substituting the given coordinates into this formula gives us |a| = sqrt((-1)^2 + (-4)^2 + 3^2) = sqrt(26). Thus, the magnitude of the vector is sqrt(26).
Step-by-step explanation:
The vector a given is a <−1, −4, 3>. To find the magnitude or length of the vector |a|, we use the formula |a| = sqrt(a1^2 + a2^2 + a3^2), where a1, a2, and a3 are the coordinates of the vector.
In our case, a1 is -1, a2 is -4 and a3 is 3. Substituting these values into the formula we get |a| = sqrt((-1)^2 + (-4)^2 + 3^2) = sqrt(1 + 16 + 9) = sqrt(26).
So the magnitude of the vector a <−1, −4, 3> is sqrt(26).
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