8. Vectors

If vector $v⃗=12î-2ĵ$ and vector $u⃗=5î+20ĵ$ calculate $2v ⃗-2u ⃗$ using $î$ and $ĵ$ notation.

If vector $v ⃗=$ $11ĵ$ and vector $u⃗=$ $10î-25ĵ$ calculate $v⃗+\(\frac\)15u⃗$ using $î$ & $ĵ$ notation.

If vector $a⃗=20î$ and vector $b⃗=50ĵ$ calculate $a ⃗-b ⃗$ using $î$ and $ĵ$ notation.

Find the unit vector in the direction of $a⃗=6î+3ĵ$.

Find the unit vector in the direction of $v⃗=12î-35ĵ$.

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

v = -5j

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

v = 8i - 6j

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

v = 4i - 2j

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

v = i - j

The magnitude and direction angle of v are ||v|| = 12 and θ = 60°. Express v in terms of i and j.

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

In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°

In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 1/2, θ = 113°