Question : Use the given vectors to find the indicated expression. : 2162321

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the given vectors to find the indicated expression.

1) v = -4i - 5j + k, w = 5i + 2j - k

Find (4v) × w.

A) 18i - 11j - 7k

B) 12i + 4j + 68k

C) -3i + 16j + 92k

D) -12i + 96j - 68k

2) v = 5i - 4j + 3k, w = 3i - 2j - 5k

Find v × (3w).

A) 78i + 102j + 6k

B) 38i + 52j + 26k

C) 66i + 84j - 18k

D) -78i - 120j - 6k

3) v = 2i + 5j - 5k, u = -4i - 3j + 4k

Find v × (2u).

A) 5i + 26j + 14k

B) 10i + 24j + 28k

C) 20i - 42j - 34k

D) -10i - 24j - 28k

4) v = 3i + 4j - 2k, w = 4i + 2j + 4k, u = -5i - 2j - 4k

Find w⋅(v × u).

A) 0

B) 76  

C) 32

D) 20

5) v = 4i - 5j - 2k, w = 5i + 3j - 4k, u = -5i - 5j + 5k

Find u⋅(v × w).

A) 93

B) 75

C) 25

D) 5

6) v = -2i - 3j - 3k, w = 3i - 2j + 4k, u = -4i - 5j - 2k

Find v⋅(v × w).

A) 24

B) -24

C) 0

D) -9

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

7) Find a unit vector normal to the plane containing u = -i + j + 4k and v = 2i - 3j + k.

8) Find a unit vector normal to the plane containing u = -i + 3j - 5k and v = 2i - j + 6k.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the requested vector.

9) v = 5i - 3j + k, w = -2i - 4j - k

Find a vector orthogonal to both v and w.

A) 20i + 29j + 37k

B) 25i - 14j + 6k

C) -7i - 3j + 3k

D) 7i + 3j - 26k

10) v = -5i - 3j + k, u = -2i + 4j - 5k

Find a vector orthogonal to both v and u.

A) -5i + 9j - 9k

B) 5i - 9j - 2k

C) -14i + 18j + 20k

D) 11i - 27j - 26k

11) v = 5i - 3j + k

Find a vector orthogonal to both v and i + j.

A) i + j + 8k

B) i - j - 6k

C) 4i - 4j - 5k

D) -i + j + 8k

12) v = 5i - 5j + k

Find a vector orthogonal to both v and i + k.

A) 3i - 6j - 3k

B) -5i - 4j + 5k

C) i - j + 4k

D) 4i - 8j - 4k

13) w = 3i - 5j - k

Find a vector orthogonal to both w and j + k.

A) -4i - 3j + 3k

B) 3i + 3j - 3k

C) 3i - 3j - 4k

D) 2i - 8j - 2k

Find the area of the parallelogram.

14) P₁ (0, 0, 0), P₂ (2, -4, 1), P₃ (-1, 2, -1)

A) √(21)

B) √(5)

C) √(6)

D) √(41)

15) P₁ (0, 0, 0), P₂ (3, 4, 1), P₃ (-2, 3, 1)

A) √(14)

B) 5√(14)

C) √(26)

D) 3√(35)

16) P₁ (1, 2, 0), P₂ (-2, 4, 2), P₃ (0, -2, 3)

A) 21

B) 2√(94)

C) √(17)

D) √(26)

17) P₁ (-1, 0, 2), P₂ (3, 2, -2), P₃ (2, -1, 3)

A) √(139)

B) 6

C) √(11)

D) 6√(10)

Find the area of the parallelogram with vertices P₁, P₂, P₃, and P₄.

18) P₁ = (7, -5, 5), P₂ = (1, 1, -4), P₃ = (9, 2, -1), P₄ = (3, 8, -10)

A) 81

B) (105/2)

C) (81/2)

D) 105