Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r ^ , u ^ , and t ^ , respectively. Consider the quantity ( − 3 u ^ × 2 t ^ ) . ( i ) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? ( ii ) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?
Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are r ^ , u ^ , and t ^ , respectively. Consider the quantity ( − 3 u ^ × 2 t ^ ) . ( i ) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? ( ii ) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?
Solution Summary: The author explains that the magnitude of the resultant vector is 6. The correct option is (a) and the incorrect option (d).
Let us name three perpendicular directions as right, up, and toward you as you might name them when you are facing a television screen that lies in a vertical plane. Unit vectors for these directions are
r
^
,
u
^
, and
t
^
, respectively. Consider the quantity
(
−
3
u
^
×
2
t
^
)
. (i) Is the magnitude of this vector (a) 6, (b) 3, (c) 2, or (d) 0? (ii) Is the direction of this vector (a) down, (b) toward you, (c) up, (d) away from you, or (e) left?
Vector A can be expressed in (i,j,k) notation as 5.0i - 4.0j, and vector B as -7.0i + 2.0j.
Determine the value of 3A + 2B in terms of magnitude and angle.
The angle can be specified either as a value between 0 and 360 degrees counter-
clockwise with respect to the positive x-axis, or as a value between 0 and 90 degrees
in the appropriate Cartesian quadrant.
Paragraph
I
+ v
...
96%
75°F
lılı
For the vectors in the figure, with a 12, b-9.0, and c-15 what are (a) the magnitude and (b) the direction of a x b. (c)
the magnitude and (d) the direction of ax, and (e) the magnitude and (f) the direction bx ?
A
(a)
(b)
(c)
(d)
(e)
(f)
108
37
i 108
Two vectors are given by A = 3 î + 6j and B = -1 î + j.
(a) Find A x
(b) Find the angle between A and
Chapter 10 Solutions
Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.