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!!!
(1)
is the increase in altitude of the sister with respect to its initial position.
the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
