Math Problem Statement

Let 

Bold w

equalsminusBold iminus6Bold j

Find the vector 

minus

9Bold w

.

Solution

We are given that:

w=i6j\mathbf{w} = -\mathbf{i} - 6\mathbf{j}

We need to find the vector 9w-9\mathbf{w}.

To do this, simply multiply the vector w\mathbf{w} by 9-9:

9w=9(i6j)-9\mathbf{w} = -9(-\mathbf{i} - 6\mathbf{j})

Distribute the 9-9:

9w=9i+54j-9\mathbf{w} = 9\mathbf{i} + 54\mathbf{j}

Thus, the vector 9w-9\mathbf{w} is:

9i+54j9\mathbf{i} + 54\mathbf{j}

Let me know if you'd like further explanation or have any other questions! Here's a tip:

Tip: When multiplying a vector by a scalar, simply multiply each component (i.e., each term involving i\mathbf{i}, j\mathbf{j}, etc.) by the scalar.

Here are 5 follow-up questions:

  1. What does multiplying a vector by a scalar do to the vector?
  2. How would you find the magnitude of the vector 9i+54j9\mathbf{i} + 54\mathbf{j}?
  3. How would you add two vectors in component form?
  4. What is the direction of the vector 9i+54j9\mathbf{i} + 54\mathbf{j}?
  5. How would you represent the vector 9w-9\mathbf{w} in terms of polar coordinates?

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Math Problem Analysis

Mathematical Concepts

Vectors
Scalar Multiplication

Formulas

Scalar multiplication of a vector: c * v = (c * v_x, c * v_y)

Theorems

Multiplying a vector by a scalar

Suitable Grade Level

Grades 9-11