Your answer is CORRECT. Let v⃗ be the vector with initial point (8,1) and terminal point (6,4). Express v⃗ as a linear combination of the standard unit vectors. a) v⃗ =3i⃗ −2j⃗ b) v⃗ =2i⃗ −3j⃗ c) v⃗ =2i⃗ +3j⃗ d) v⃗ =−2i⃗ −3j⃗ e) v⃗ =−2i⃗ +3j⃗ f) None of the above. Question 2 Your answer is CORRECT. Let v⃗ be the vector with initial point (−5,1) and terminal point (5,3). Find the vertical component of this vector. a) −6 b) 8 c) 2 d) −2 e) 10 f) None of the above. Question 3 Your answer is CORRECT. Find the sum of the vectors u⃗ =6i⃗ −4j⃗ and v⃗ =−2i⃗ −5j⃗ . a) v⃗ =−7i⃗ +2j⃗ b) v⃗ =4i⃗ −9j⃗ c) v⃗ =4i⃗ +4j⃗ d) v⃗ =2i⃗ −7j⃗ e) v⃗ =−9i⃗ +4j⃗ f) None of the above. Question 4 Your answer is INCORRECT. Given vectors u⃗ =⟨−2,−3⟩ and v⃗ =⟨5,2⟩; find 5u⃗ −4v⃗ . a) v⃗ =⟨22,−7⟩ b) v⃗ =⟨−30,−23⟩ c) v⃗ =⟨33,22⟩ d) v⃗ =⟨−25,−28⟩ e) v⃗ =⟨−23,−30⟩ f) None of the above. Question 5 Your answer is INCORRECT. Find the magnitude of the vector v⃗ =4i⃗ −4j⃗ . a) 8 b) 42–√ c) 32 d) −32 e) 0 f) None of the above. Question 6 Your answer is INCORRECT. Given the vector v⃗ =⟨1,3⟩; find a unit vector in the same direction as v⃗ . a) ⟨16,12⟩ b) ⟨310−−√10,10−−√10⟩ c) ⟨1,3⟩ d) ⟨10−−√10,310−−√10⟩ e) ⟨110,310⟩ f) None of the above.

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!!!

c. rb

explanation:

the atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center of the nucleus to the boundary of the surrounding shells of electrons.

this means that the temperature of both substances will be equal