Let i ^ be directed to the east, j ^ be directed to the north, and k ^ be directed upward. What are the values of products (a) i ^ · k ^ , (b) (− k ^ ) · (− j ^ ), and (c) j ^ · (− j ^ )? What are the directions (such as east or down) of products (d) k ^ × j ^ , (e) (− i ^ ) × (− j ^ ), and (f) (− k ^ ) × (− j ^ )?
Let i ^ be directed to the east, j ^ be directed to the north, and k ^ be directed upward. What are the values of products (a) i ^ · k ^ , (b) (− k ^ ) · (− j ^ ), and (c) j ^ · (− j ^ )? What are the directions (such as east or down) of products (d) k ^ × j ^ , (e) (− i ^ ) × (− j ^ ), and (f) (− k ^ ) × (− j ^ )?
Let
i
^
be directed to the east,
j
^
be directed to the north, and
k
^
be directed upward. What are the values of products (a)
i
^
·
k
^
, (b) (−
k
^
) · (−
j
^
), and (c)
j
^
· (−
j
^
)? What are the directions (such as east or down) of products (d)
k
^
×
j
^
, (e) (−
i
^
) × (−
j
^
), and (f) (−
k
^
) × (−
j
^
)?
Use the definition of scalar product, a b = ab cos 0, and the fact that a ⋅ b = axbx + ayby+ a₂b₂ to calculate
▪
the angle between the two vectors given by a
=
3.01 +3.07 + 3.0k and b
7.0î + 8.07 + 9.0k.
Number
i
Units
=
Given the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following.
(a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.) ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.) ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.) °
Given the pair of vectors, A = (9.0oî – 2.00j ) and B =
i +
(-2.00î + 7.00j ), use the definition of a scalar product to determine the following.
(a) the scalar product
(b) the angle between the vectors (Enter an answer between 0 and 180 degrees.)
(c) the angle a between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.)
(d) the angle ß between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.)
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