Consider a → in the positive direction of x , b → in the positive direction of y , and a scalar d. What is the direction of b → /d if d is (a) positive and (b) negative? What is the magnitude of (c) a → · b → and (d) a → · b → /d ? What is the direction of the vector resulting from (e) a → × b → and (f) b → × a → ? (g) What is the magnitude of the vector product in (e)? (h) What is the magnitude of the vector product in (f)? What are (i) the magnitude and (j) the direction of a → × b → /d if d is positive?
Consider a → in the positive direction of x , b → in the positive direction of y , and a scalar d. What is the direction of b → /d if d is (a) positive and (b) negative? What is the magnitude of (c) a → · b → and (d) a → · b → /d ? What is the direction of the vector resulting from (e) a → × b → and (f) b → × a → ? (g) What is the magnitude of the vector product in (e)? (h) What is the magnitude of the vector product in (f)? What are (i) the magnitude and (j) the direction of a → × b → /d if d is positive?
Consider
a
→
in the positive direction of x
,
b
→
in the positive direction of y, and a scalar d. What is the direction of
b
→
/d if d is (a) positive and (b) negative? What is the magnitude of (c)
a
→
·
b
→
and (d)
a
→
·
b
→
/d? What is the direction of the vector resulting from (e)
a
→
×
b
→
and (f)
b
→
×
a
→
? (g) What is the magnitude of the vector product in (e)? (h) What is the magnitude of the vector product in (f)? What are (i) the magnitude and (j) the direction of
a
→
×
b
→
/d if d is positive?
The magnitudes of two vectors A → a n d B → are 12 units and 8 units, respectively. What are the largest and smallest possible values for the resultant vector R → = A → + B →?
Consider vectors A = -51 + 2j and B = 6î – 5j. Now answer the following questions
a. In which quadrant does vector A and B lie. What are the x and y coordinates of A and B?
b. Show A+ B graphically and calculate A+Balgebraically?
Use Equations (3) to generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then generate another parametrization of the line using the point P2(-2, -2, 1) and the vector v2 = -i + (1/2)j - (3/2)k.
University Physics with Modern Physics (14th Edition)
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