Question

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.

Answer 1

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!!!