1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Galina-37 [17]
2 years ago
12

If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by​

Mathematics
1 answer:
PIT_PIT [208]2 years ago
7 0

Answer:

The family of possible values for p are:

(-\infty, -4) \,\cup \,(7, +\infty)

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|} (1)

Where:

\theta - Angle between vectors, in sexagesimal degrees.

\|\vec a\|, \|\vec b \| - Norms of vectors \vec {a} and \vec{b}

If \theta is acute, then the cosine function is bounded between 0 a 1 and if we know that \vec {a} = (p, 3, -7) and \vec {b} = (p, -p, 4), then the possible values for p are:

Minimum (\cos \theta = 0)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0

Maximum (\cos \theta = 1)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1

With the help of a graphing tool we get the family of possible values for p are:

(-\infty, -4) \,\cup \,(7, +\infty)

You might be interested in
A statement of an employee’s biweekly earnings is given below. What is the employee’s gross pay?
Olin [163]
The employee's gross pay
$726.80
3 0
3 years ago
Draw an arc about point A so that it intersects the two sides of angle A. Label the intersection points B and C
joja [24]
Dqw23532424524624344352346246b 
5 0
3 years ago
Help please help me please
allsm [11]

Answer:

A. 2 (0)=0

B. 2 (2)=4

Step-by-step explanation:

You have to multiply the X numbers by 2 for example 2x , x=2 , 2x2=4

8 0
2 years ago
Prove that the decimal 8.72 is rational by finding its fractional form.
Marizza181 [45]
Noce


Step by step solution



Dd
D
D
Dd
D
F
6 0
3 years ago
The area of this rectangle is 4x2
meriva

Answer:

8 units squared.

Step-by-step explanation:

Assuming the numbers are the length and width, we can use the formula for finding the area of the rectangle.

The area should be eight units squared.

a = l * w\\a = 4 * 2\\a= 8

3 0
3 years ago
Other questions:
  • Anais bought 3½ yards of ribbon. She had 2 feet 10 inches of ribbon left after trimming some curtains. How many inches of ribbon
    13·1 answer
  • Write this number in standard notation.<br><br>1.986 x 10^6
    13·2 answers
  • Look at this equation. 3(x + 1) = 3x + Which number can be placed in the box that would create an equation that has an infinite
    12·2 answers
  • What is 250(1+0.018/2)^2t in written form?
    15·1 answer
  • Find the product of 30x10
    5·2 answers
  • Under which isometry is the slope of line segment equal to the slope of it's image?
    15·1 answer
  • Help me with this pls
    13·2 answers
  • PLEASE HELP WILL MAKE BRAINILEST ALSO PLEASE SHOW UR WORK TYSM
    15·2 answers
  • 384,000 in scientific notaion
    9·1 answer
  • If the measurement of angle a is 113°, then what is the measurement of angle d ? Question 20 options: 67° 23° 113° 100°
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!