Logs and Vectors

Quaternions

100

This one is not true: ij=k, kj=-i, ki=j, or jk=-i.

What is jk=-i?

200

If q = a + bi + cj + dk is the conjugate of p = 2 + 3i - 5j + 6k, then a + b + c + d is...

What is -2?

300

u = 2i and v = 3 + 2i - 5j, so uv = ?

What is -4 + 6i - 10k?

400

u = 2 + i and v = 8 + 3j, then vu = ?

What is 16 + 8i + 6j - 3k?

500

The inverse of q = 2 + 3i - 4j + k.

What is 1/15 - 1/10 i + 2/15 j - 1/30 k?

Simplifying logs

100

log3 + 4log x - 7log y

What is log (3x⁴y^-7)?

200

lnx + 1/2 ln (y² + z²)

What is ln (x sqrt(y² + z²))?

300

log₄ (x - 4) - 2log₄ y - 1/5 log₄ z

log₄ [(x - 4)/y² (5rt z)]

400

3 ln (t + 5) - 4 ln t - 2 ln (s-1)

What is ln [(t+5)³/t⁴ (s-1)²]?

500

1/3 log a - 6 log b +2

What is log [(100 3rt(a))/b⁶]?

Log Algebra

100

The solution(s) for log₄ (x² - 2x) = log₄ (5x - 12).

What are x = 3 and x = 4?

200

The solution(s) for log (6x) - log (4 - x) = log 3.

What is x = 4/3?

300

The solution(s) for log₃(25-x²) = 2.

What are x = 4 and x = -4?

400

The solution(s) for log₄ (-x) + log₄ (6 - x) = 2.

What is x = -2?

500

The solution(s) for 2 log (x) - log (7x - 1) = 0.

What are x = 0.1459 and x = 6.8541?

Vector Word Problems

100

The size and direction of the resultant force on a box if one boy pushes with 125 N to the east and one pushes 165 N to the north.

What is 207 N and 52.85^o?

200

The resulting displacement for an explorer who walks 13 km due east, then 18 km north, and finally 3 km west.

What is 20.59 km at 60.95^o?

300

The component of the plane's velocity toward 90^o for a plane flying toward 149^o at 525 km/h.

What is 270.39 km/h?

400

The resultant force on a crate being pushed by Dion (185 N, 0^o), Shirley (164 N, 30^o), and Joan (195 N, 300^o).

What is 433.33 N at -11.56^o (348.44^o)?

500

The force that produces equilibrium on an object under a horizontal force of 6 N and a vertical force of 8 N.

What is 10 N at 233.13^o (-126.87^o)?

Awesome Vectors(lines, planes)

100

The line that is parallel to x = 3 - t, y = 6t, z = 7t + 2, and goes through the point P(0, 1, 2).

What is x = -t, y = 1 + 6t, z = 2 + 7t?

200

The line that is orthogonal to the plane 3x - y + 2z = 10 and goes through the point P(1, 4, -2).

What is x = 1 + 3t, y = 4 - t, z = -2 + 2t?

300

The equation of the plane that goes through A(1, 0, 2), B(2, 1, 0), and C(-1, 6, 4).

What is 14x + 2y + 8z = 30?

400

The equation of the plane that is orthogonal to the line x = 4 + t, y = 1 - 2t, z = 8t and goes through the point P(4, -1, 2).

What is x - 2y + 8z - 7 = 0?

500

The equation of the plane that is parallel to the plane 5x - 3y + 2z = 6 and goes through the point P(4, -1, 2).

What is 5x - 3y + 2z = 27?