Find the unit vector in the direction of vector D = -3i + 4j.

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Question: Find the unit vector in the direction of vector D = -3i + 4j.

Options:

Correct Answer: -0.6i + 0.8j

Solution:

Magnitude |D| = √((-3)^2 + 4^2) = √(9 + 16) = √25 = 5. Unit vector = D/|D| = (-3/5)i + (4/5)j = -0.6i + 0.8j.

Find the unit vector in the direction of vector D = -3i + 4j.

Find the unit vector in the direction of vector D = -3i + 4j.

Step 1: Identify the vector D. Here, D = -3i + 4j.
Step 2: Calculate the magnitude of vector D using the formula |D| = √(x^2 + y^2), where x and y are the coefficients of i and j.
Step 3: Substitute the values into the formula: |D| = √((-3)^2 + 4^2).
Step 4: Calculate (-3)^2, which is 9, and 4^2, which is 16.
Step 5: Add the results: 9 + 16 = 25.
Step 6: Take the square root of 25 to find the magnitude: √25 = 5.
Step 7: To find the unit vector, divide each component of vector D by its magnitude: Unit vector = D/|D|.
Step 8: Calculate the unit vector: (-3/5)i + (4/5)j.
Step 9: Simplify the fractions: -3/5 = -0.6 and 4/5 = 0.8.
Step 10: Write the final unit vector as -0.6i + 0.8j.

Vector Magnitude – Understanding how to calculate the magnitude of a vector using the Pythagorean theorem.
Unit Vector – Knowing how to find a unit vector by dividing a vector by its magnitude.