Jeopardy! for the Classroom

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Presentation transcript:

Jeopardy! for the Classroom

C & V Vectors The Dot Product The Cross Product Mixed Bag 100 200 300 Vectors in Space The Cross Product Mixed Bag C & V 100 200 300 400 500

Given v and w , graph v-w.

v v - w -w

The vector whose initial point is (-3,2) and terminal point is (-6,5)

What is v = -3i + 3j?

||v|| given v = -4i + 5j

What is √41?

The unit vector having the same direction as v = 12i - 5j

What is v = <12/13, -5/13> ?

Given v = 2i – j and w = i – j, find 2||v – 3w||.

What is 2√5?

Given v = 2i + 2j and w = i + 2j, find the dot product.

What is 6?

Given v·w = - 12, ||v|| = 2, and ||w|| = 6, v and w are parallel, orthogonal, or neither.

What is parallel?

Given v = 2i + j and w = i + 2j, find the angle between v and w.

What is 36.87°?

Given -3v = w, v and w are parallel, orthogonal, or neither.

What is parallel?

Given v = i – k and w = 2j + 3k, find v·w.

What is -3?

The exact distance between (-2, 2, 3) and (4, 0, -2)

What is √65?

The vector whose initial point is (-1, 4, -2) and terminal point is (6, 2, 2)

What is 7i – 2j + 4k?

Given v = -2i + 3j - 2k and w = 3i – 5j + 2k, find ||v – w||.

What is √105?

The unit vector having the same direction as v = 3i – 6j – 2k

What is v = 3/7i – 6/7j – 2/7k?

Given v = - i + 3j + 2k and, find the direction angle α.

What is 105.5°?

Given v = -4i + 3j – 5k, find v x v.

What is 0?

Given v = 2i - 3j and w = 3j + k, find v x w.

What is -3i – 2j + 6k?

Given v = 2i - 3j and w = 3j + k, find w x v.

What is 3i + 2j – 6k?

Given u = 2i – 3j + k, v = -3i + 3j + 2k, and w = i + j + k, find u·(v x w).

What is -19?

The vector that is orthogonal to v = 2i – j – k and w = i + 2j +2k

What is – 5j + 5k?

The position vector form of a vector with a magnitude of 6 and direction of 120°

What is -3i + 3√3j?

The dot product of two orthogonal vectors

What is 0?

Daily Double

A vector whose magnitude is zero

What is a zero vector?

The result of a cross product

What is a vector?

Given v = - i + 3j +2k and w = i – j + k, find the angle between v and w.

What 107.98°?

A quantity with magnitude and direction

What is a vector?

A vector with a magnitude of one

What is a unit vector?

A vector whose initial point is at the origin

What is a position vector?

Two vectors with an angle of 90° between them

What is orthogonal?

The result of a dot product

What is a scalar?

Final Jeopardy!

Airplanes!

An airplane has an airspeed of 500 kph going due north An airplane has an airspeed of 500 kph going due north. The wind velocity is a constant 70 kph from the east. Find the actual speed and direction of the plane relative to the ground.

What is 504.9 kph at N7.97°W?