If | vector a | = 4 and –3 ≤ λ ≤ 2, then write the range of |λ vector a|.

Question

If | \(\vec a\) | = 4 and  –3 ≤ λ ≤ 2, then write the range of |λ \(\vec a\)|.

Answer 1

Given that   | \(\vec a\) | = 4 and  –3 ≤ λ ≤ 2,

We have to figure out range of \(|\,\lambda\vec a\,|\).

In calculating the modulus of a vector multiplied by a scalar quantity, the sign of the scalar quantity does not matter, only it’s absolute value does.

Hence the minimum value of \(|\,\lambda\vec a\,|\) = 0 when λ=0 and maximum value of \(|\,\lambda\vec a\,|\) = 12 when λ=-3.