Question

Determine the magnitudes of the following vectors;

(i) 𝑨⃗⃗ =(𝟐𝒊̂+𝟑𝒋̂+𝟔𝒌̂)

(ii) 𝑩⃗⃗ =(𝟑𝒊̂+𝟗𝒋̂−𝟔𝒌̂)

(iii) 𝑪⃗⃗ =(𝟑𝒊̂−𝟓𝒋̂+𝒌̂)

(iv) 𝑫⃗⃗ =(𝟖𝒊̂−𝟒𝒋̂+𝟖𝒌̂)

Answer 1

The magnitude of vector is:

$$a = \sqrt{a_x^2 + a_y^2 + a_z^2}$$

where $a_x, a_y, a_z$ are coordinates of the vector. Thus, for the given vectors obtain:

$$A = \sqrt{2^2 + 3^2 + 6^2} = 7\\ B = \sqrt{3^2 + 9^2 + (-6)^2} \approx 11.2\\ C = \sqrt{3^2 + (-5)^2 + 1^2} \approx 5.9\\ D = \sqrt{8^2 + (-4)^2 + 8^2} = 12$$

Answer. 7, 11.2, 5.9, 12.