Answer:
1) Option E is correct.
vector v = (-2î + 3ĵ)
2) Option C is correct.
The vertical component of vector v = 2
3) Option B is correct.
The vector sum of u and v = (4î - 9ĵ)
4) Option B is correct.
5u - 4v = (-30î - -23ĵ)
5) Option F is correct.
Magnitude of v = √32 units = 4√2 units = 5.66 units
6) Option F is correct.
Unit vector in the same direction as v is
v = (î + 3ĵ)/√10 = [(1/√10), (3/√10)]
Explanation:
1) vector v has initial point (8,1) and terminal point (6,4)
Write vector v as a linear combination of the standard unit vector.
v represented in standard form is given as
Vector v = (final position vector) - (initial position vector) = (6î + 4ĵ) - (8î + ĵ) = (-2î + 3ĵ)
2) v be the vector with initial point (−5,1) and terminal point (5,3). Find the vertical component of this vector.
v represented in standard form is given as
Vector v = (final position vector) - (initial position vector) = (5î + 3ĵ) - (-5î + ĵ)
v = (10î + 2ĵ)
The vertical component is the ĵ-component and it is equal to 2
3) Find the sum of the vectors u =6i −4j and v⃗ =−2i −5j
Vector sum is done on a per component basis
Sum = u + v = (6î - 4ĵ) + (-2î - 5ĵ) = (4î - 9ĵ)
4) Given vectors u⃗ =⟨−2,−3⟩ and v⃗ =⟨5,2⟩; find 5u⃗ −4v⃗
u = (-2î - 3ĵ)
v = (5î + 2ĵ)
5u - 4v = 5(-2î - 3ĵ) - 4(5î + 2ĵ)
= (-10î - 15ĵ) - (20î + 8ĵ)
= (-30î - 23ĵ)
5) Find the magnitude of the vector v = (4i−4j)
Magnitude of a vector is given as
/v/ = √[vₓ² + vᵧ²]
where vₓ and vᵧ are x and y components of the velocity.
/v/ = √[(4²) + (-4)²] = 4√2 units = 5.66 units
6) Given the vector v =⟨1,3⟩; find a unit vector in the same direction as v
Unit vector in the direction of a vector = (vector)/(magnitude of vector)
Vector v = (î + 3ĵ)
Magnitude of vector v = √[1² + 3²] = √10
Unit vector in the same direction as v = (î + 3ĵ)/√10
Hope this Helps!!!
