8. Vectors

In Exercises 39–46, find the unit vector that has the same direction as the vector v.

v = 3i - 4j

In Exercises 39–46, find the unit vector that has the same direction as the vector v.

v = 3i - 2j

In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 6, θ = 30°

In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. ||u + v||² - ||u - v||²

In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = -10i + 15j

In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - u. Use vector notation as in Example 4.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - u. Use vector notation as in Example 4.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.