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kkurt [141]
3 years ago
15

Show that (×)× = ×(×) if and only if the vectors and are collinear.

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

Step-by-step explanation:

<em>NOTE: Bolded letters are vectors</em>

Given that ,

  • (axb)xc = ax(bxc)

From vector triple product rule,

  • ax(bxc) = b(a.c)-c(a.b)
  • ax(bxc) = b(a.c)-a(b.c)

If these both are equal, then :

⇒b(a.c)-c(a.b) = b(a.c)-a(b.c)

⇒(-a.b)c = (-b.c)a

⇒(|a||b|sin∅)c = (|b||c|sinФ)a (cancel |b| on both sides)

A , C are the unit vectors of a and c respectively .

Two vectors can be equal on when their magnitude and directions are same.

That is when ,

⇒(|a||c|sin∅)A = (|a||c|sinФ)C

⇒sin∅A = sinФC

This can only be possible when the vectors are collinear because the angle made by the vectors with the vector B should be the same or supplementary and the vectors A and C must be in the same direction.

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A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 210 feet (ft). If the wheel
frutty [35]

Answer:

The change in the height of the seat of the Ferris wheel is a reduction in height of approximately 74.25 feet

Step-by-step explanation:

The given information are;

The position of the seat on the Ferris wheel = The center level of the wheel

The diameter of the Ferris wheel = 210 feet

The angle of rotation of the wheel = 45° counterclockwise

The height of a point on the Ferris wheel is given by the relation;

h = A·cos(b·x + c) + d

With regards to the question, we have;

h = The height of the seat of the Ferris wheel

A = The amplitude = 1/2 × The diameter of the wheel = 210/2 = 105 feet

360/b = The period

c = The phase shift = 90°

d = The mid line = 0

For a rotation of 45° counterclockwise or-45° clockwise, we have;

b·x = 45°, therefore;

h  = 105 × cos(45° + 90°) + 0 = 105 × cos(135°) + 0

h = 105 × cos(135°) ≈ -74.25 feet

Therefore, the height of the seat of the Ferris wheel reduces by 74.246 feet.

6 0
3 years ago
How do you slove 2/3 (9x -6) = 14
Ivanshal [37]

Answer:

x=3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2

3

(9x−6)=14

(

2

3

)(9x)+(

2

3

)(−6)=14(Distribute)

6x+−4=14

6x−4=14

Step 2: Add 4 to both sides.

6x−4+4=14+4

6x=18

Step 3: Divide both sides by 6.

6x

6

=

18

6

x = 3

5 0
3 years ago
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pshichka [43]

Answer:

Step-by-step explanation:

6 0
3 years ago
A menu has three meat choices,
wolverine [178]

Answer:

18 ways

Step-by-step explanation:

Number of Meat choices = 3

Number of Vegetable choices = 3

Number of Desserts = 2

Number of ways dinner can be chosen :

Number of meat choices * Number of vegetable choices * number of desserts

3 * 3 * 2

= 18

Hence, dinner can be chosen in 18 different choices.

4 0
2 years ago
What is the equation, in slope-intercept form, of the line that passes through the point (3, −3) and is perpendicular to the lin
jonny [76]

Answer:

i have no clue.

Step-by-step explanation:

good luck

5 0
3 years ago
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