Chat with AIExam 13: Vector Geometry
Exam 1: Precalculus Review74 Questions
Exam 2: Limits97 Questions
Exam 3: Differentiation81 Questions
Exam 4: Applications of the Derivative77 Questions
Exam 5: The Integral82 Questions
Exam 6: Applications of the Integral80 Questions
Exam 7: Exponential Functions106 Questions
Exam 8: Techniques of Integration101 Questions
Exam 9: Further Applications of the Integral and Taylor Polynomials100 Questions
Exam 10: Introduction to Differential Equations73 Questions
Exam 11: Infinite Series95 Questions
Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections71 Questions
Exam 13: Vector Geometry96 Questions
Exam 14: Calculus of Vector-Valued Functions99 Questions
Exam 15: Differentiation in Several Variables95 Questions
Exam 16: Multiple Integration98 Questions
Exam 17: Line and Surface Integrals92 Questions
Exam 18: Fundamental Theorems of Vector Analysis91 Questions
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Consider the parallel lines 
and 
Compute the distance 
between the two lines using the following steps.
A) Choose any two points 
and 
on 
B) Choose any point 
on 
C) Compute the area of the triangle 
, the length of 
, and find the height from 
to 
, using the area of a triangle.
D) What is the distance between 
and 
?
and Compute the distance between the two lines using the following steps.
A) Choose any two points and on
B) Choose any point on
C) Compute the area of the triangle , the length of , and find the height from to , using the area of a triangle.
D) What is the distance between and ?
Free
(Essay)
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(34) Correct Answer:
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Let 
and 
be two nonzero orthogonal vectors.
A) Find 
in terms of 
, 
, and 
B) Find the scalar 
such that 
C) If 
and 
are orthogonal unit vectors, write the area of the parallelogram spanned by 
and 
in terms of 
only.
and be two nonzero orthogonal vectors.
A) Find in terms of , , and
B) Find the scalar such that
C) If and are orthogonal unit vectors, write the area of the parallelogram spanned by and in terms of only.Free
(Essay)
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(26) Correct Answer:Verified
VerifiedA) 
B) 
C) 
Convert the point 
from cylindrical coordinates to rectangular coordinates.
from cylindrical coordinates to rectangular coordinates.Free
(Essay)
4.9/5 (32)
(32) Correct Answer:Verified
Verified
, and 
lie in one plane.
for which 
is parallel to 
where 
Compute the height 
to the side 
in the triangle with vertices at 
, 
, and 
.
to the side in the triangle with vertices at , , and . (Essay)
4.7/5 (33)
(33) Let 
and 
.
A) Write the coordinates of the point 
on 
lying three-fifths of the way from 
to 
.
B) Write 
as a linear combination of 
and 
.
and .
A) Write the coordinates of the point on lying three-fifths of the way from to .
B) Write as a linear combination of and . (Essay)
4.9/5 (32)
(32) Find scalars 
, and 
such that:
A) 
is parallel to 
.
B) 
has the same length as 
.
C) 
is a unit vector.
, and such that:
A) is parallel to .
B) has the same length as .
C) is a unit vector. (Essay)
4.9/5 (32)
(32) The angle between two intersecting lines is the acute angle between the direction vectors of the lines. Find the angle between the line through the points 
and 
and the line through the points 
and 
.
and and the line through the points and . (Essay)
4.7/5 (33)
(33) Convert the point 
from cylindrical coordinates to spherical coordinates.
from cylindrical coordinates to spherical coordinates. (Essay)
4.9/5 (36)
(36) 
, and 
.Consider the points 
, 
, 
, and 
. Find the length of the vector starting at the midpoint of 
and ending at the midpoint of 
.
, , , and . Find the length of the vector starting at the midpoint of and ending at the midpoint of . (Essay)
4.8/5 (32)
(32) Write the equation of the quadric surface 
in standard form, and identify its type.
in standard form, and identify its type. (Essay)
4.8/5 (32)
(32) The angle between 
and 
is 
and 
Let 
and 
be the vectors 
and 
.
A) Find the dot product 
B) Find the dot product 
and use it to compute the lengths 
and 
C) Find the angle between 
and 
and is and Let and be the vectors and .
A) Find the dot product
B) Find the dot product and use it to compute the lengths and
C) Find the angle between and (Essay)
4.8/5 (31)
(31) On a two-dimensional Cartesian coordinate system, 
is the position vector from the origin to the point 
and 
is the position vector with length 
at an angle 
to the positive x-axis. Find the vectors.
A) 
B) 
is the position vector from the origin to the point and is the position vector with length at an angle to the positive x-axis. Find the vectors.
A)
B) (Essay)
4.8/5 (39)
(39) 
, and 
.
and 
intersect if:Find an equation of the plane passing through the points 
and 
and with the vector 
lying on the plane.
and and with the vector lying on the plane. (Essay)
4.8/5 (29)
(29) Compute the area of the projection onto the xy-plane of the parallelogram spanned by the vectors 
and 
.
and . (Short Answer)
4.9/5 (37)
(37) Consider the following two lines. 
The two lines intersect if:
The two lines intersect if: (Multiple Choice)
4.7/5 (26)
(26) 
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