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Quiz

Lesson 1 Quiz: Three-Dimensional Cartesian Coordinates and Vector Operations

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  • Questions count: 10
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1.
If vector A = (2, -1, 3) and vector B = (k, 4, -2) are perpendicular, what is the value of k?
-5
-10
5
10
2.
The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:
r = -1/2
r = 4
r = 2
r = 1/2
3.
The sum to infinity (S_infinity) of a geometric series exists and converges if and only if the common ratio satisfies:
r > 1
|r| >= 2
r = 1
|r| < 1 (i.e. -1 < r < 1), and S_infinity = a / (1 - r)
4.
The sum to infinity of the geometric series 12 + 6 + 3 + 1.5 + ... equals:
18
24
Infinity
36
5.
The sum of the first 10 terms of the geometric sequence 2, 6, 18, 54, ... equals:
59,048
118,096
19,682
29,524
6.
The 7th term of the geometric sequence (2, 6, 18, ...) is:
486
729
1458
162
7.
The sum to infinity of the geometric series 16 + 8 + 4 + 2 + ... equals:
24
30
32
64
8.
If two vectors \(\vec{A} = (2, k, -3)\) and \(\vec{B} = (4, 2, 6)\) are perpendicular, then the value of \(k\) is:
C) 10
D) -10
A) 5
B) -5
9.
The vector product \(\vec{A} \times \vec{B}\) geometrically represents:
C) The work done by vector $vec{A}$ along $vec{B}$
D) The scalar projection of $vec{A}$ on $vec{B}$
B) A vector perpendicular to both $vec{A}$ and $vec{B}$ with magnitude equal to the area of the spanned parallelogram
A) The angle between the two vectors
10.
If \(\alpha, \beta, \gamma\) are the direction angles of a vector, then \(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma\) equals:
D) 3
A) 0
B) 1
C) 2
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