MAC 2313 Exam 1 (Actual Exam 2025) | Complete Questions and
Correct answers | Graded A+ | Latest Version | Verified Answers |
Brand New Version!
The magnitude of a vector is the _______________ - correct answer length of the vector/line
segment
The direction of a vector is the __________ - correct answer direction of the arrow
A negative vector is ______________ - correct answer just a vector going in the opposite
direction
To calculate a vector: ________ point - _________ point - correct answer terminal point - initial
point
To calculate the magnitude of a vector you use the _____________ formula - correct answer
distance
v+w - correct answer <x1 + x2, y1 + y2, z1 + z2>
v-w - correct answer <x1 - x2, t1 - y2, z1 - z2>
cv - correct answer <cx, cy, cz>
(u + v) + w - correct answer u + (v + w)
v + 0 - correct answer v
v + (-v) - correct answer 0-vector
c(u + v) - correct answer cu + cv
(a+c)v - correct answer av + cv
0v - correct answer 0-vector
c0 - correct answer 0-vector
1v - correct answer v
a(c*v*) - correct answer (ac)*v*
A unit vector is a vector of length _________ - correct answer one
How d o you calculate a unit vector? - correct answer vector / magnitude of the vector
a unit vector is written as __________ - correct answer vector hat ^w
, The standard unit vectors are given by:
i = _____________
j = _____________
k= _____________ - correct answer i = <1, 0, 0>
j = <0, 1, 0>
k= <0, 0, 1>
Two vectors are parallel if one is a ___________ _____________ of the other - correct answer
scalar multiple
The zero vector is parallel to _____________ vector - correct answer every
Two vectors are equivalent if they _____________________________ and have the same
______________ - correct answer point in the same direction and have the same magnitude
The net force on an object is the ___________________ of all forces acting on the object -
correct answer vector sum
Dot product: u * v = - correct answer x1 @ x2 + y1 @ y2 + z1 @ z2
The dot product is also referred to as the ______________ or ______________ product -
correct answer inner or scalar product
0 * v - correct answer o vector
v * w - correct answer w * v
(scalar @ v) @ w - correct answer scalar( w @ v) or v @ (scalar @ w)
u * (v + w) - correct answer u * v + u * w
(v + w) * u - correct answer v * u + w* u
v * v - correct answer | v | ^2
|v| - correct answer sqrt: v * v
theorem: v @ w - correct answer |v| @ |w| @ cos(theta)
Two vectors are orthogonal/perpendicular if their dot product is equal to __________ - correct
answer zero
the zero vector is ____________ to all other vectors - correct answer orthogonal
What is the vector projection of b onto a? - correct answer the part of b parallel to a
Correct answers | Graded A+ | Latest Version | Verified Answers |
Brand New Version!
The magnitude of a vector is the _______________ - correct answer length of the vector/line
segment
The direction of a vector is the __________ - correct answer direction of the arrow
A negative vector is ______________ - correct answer just a vector going in the opposite
direction
To calculate a vector: ________ point - _________ point - correct answer terminal point - initial
point
To calculate the magnitude of a vector you use the _____________ formula - correct answer
distance
v+w - correct answer <x1 + x2, y1 + y2, z1 + z2>
v-w - correct answer <x1 - x2, t1 - y2, z1 - z2>
cv - correct answer <cx, cy, cz>
(u + v) + w - correct answer u + (v + w)
v + 0 - correct answer v
v + (-v) - correct answer 0-vector
c(u + v) - correct answer cu + cv
(a+c)v - correct answer av + cv
0v - correct answer 0-vector
c0 - correct answer 0-vector
1v - correct answer v
a(c*v*) - correct answer (ac)*v*
A unit vector is a vector of length _________ - correct answer one
How d o you calculate a unit vector? - correct answer vector / magnitude of the vector
a unit vector is written as __________ - correct answer vector hat ^w
, The standard unit vectors are given by:
i = _____________
j = _____________
k= _____________ - correct answer i = <1, 0, 0>
j = <0, 1, 0>
k= <0, 0, 1>
Two vectors are parallel if one is a ___________ _____________ of the other - correct answer
scalar multiple
The zero vector is parallel to _____________ vector - correct answer every
Two vectors are equivalent if they _____________________________ and have the same
______________ - correct answer point in the same direction and have the same magnitude
The net force on an object is the ___________________ of all forces acting on the object -
correct answer vector sum
Dot product: u * v = - correct answer x1 @ x2 + y1 @ y2 + z1 @ z2
The dot product is also referred to as the ______________ or ______________ product -
correct answer inner or scalar product
0 * v - correct answer o vector
v * w - correct answer w * v
(scalar @ v) @ w - correct answer scalar( w @ v) or v @ (scalar @ w)
u * (v + w) - correct answer u * v + u * w
(v + w) * u - correct answer v * u + w* u
v * v - correct answer | v | ^2
|v| - correct answer sqrt: v * v
theorem: v @ w - correct answer |v| @ |w| @ cos(theta)
Two vectors are orthogonal/perpendicular if their dot product is equal to __________ - correct
answer zero
the zero vector is ____________ to all other vectors - correct answer orthogonal
What is the vector projection of b onto a? - correct answer the part of b parallel to a
