Question

Найдите | a− 3⃗b |, если a {–2; 11; 2},b {1; 4; –1}

Answer 1

{–2; 11; 2}-3{1; 4; –1}={–2; 11; 2}- {3;12; –3}={-5;-1; 5}

| a− 3⃗b |=√(25+1+25)=√51

Answer 2

To find the magnitude of the vector subtraction |a - 3b|, we first need to calculate the vector a - 3b, and then find its magnitude.

Given: a = {-2, 11, 2} b = {1, 4, -1}

Step 1: Calculate a - 3b To subtract two vectors, we subtract the corresponding components:

a - 3b = {-2, 11, 2} - 3{1, 4, -1} = {-2, 11, 2} - {3, 12, -3} = {-2-3, 11-12, 2-(-3)} = {-5, -1, 5}

Step 2: Calculate the magnitude of the vector {-5, -1, 5} The magnitude (or length) of a vector can be calculated using the Euclidean norm formula:

|v| = sqrt(v1^2 + v2^2 + v3^2)

|{-5, -1, 5}| = sqrt((-5)^2 + (-1)^2 + 5^2) = sqrt(25 + 1 + 25) = sqrt(51) ≈ 7.1414

Therefore, the magnitude of the vector a - 3b is approximately 7.1414.