If a = (4, 0, 3) and b = (-2, 1, 5) find |a|, the vector a – b and 2a + b

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Solution:

Given vectors are

a = (4 , 0, 3)

b = (-2, 1, 5)

Now,

\(|\vec{a}| = \sqrt{4^2 + 0^2 + 3^2} = 5 \enspace units\)

\(\vec{a} – \vec{b}\) = (4 , 0, 3) – (-2, 1, 5) = (6, -1, -2)

\(2\vec{a} + 5\vec{b}\) = 2(4 , 0, 3) – 5(-2, 1, 5)

= (8, 0, 6) + (-10, 5, 25)

= (-2, 5, 31)

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