(a) In unit-vector notation, what is r → = a → − b → + c → if a → = 5.0 i ^ + 4.0 j ^ − 6.0 k ^ , b → = − 2.0 i ^ + 2.0 j ^ + 3.0 k ^ , and c → = 4.0 i ^ + 3.0 j ^ + 2.0 k ^ ? (b) Calculate the angle between r → and the positive z axis. (c) What is the component of a → along the direction of b → ? (d) What is the component of a → perpendicular to the direction of b → but in the plane of a → and b → ? ( Hint: For (c), see Eq. 3-20 and Fig. 3-18; for (d), see Eq. 3-24.)
(a) In unit-vector notation, what is r → = a → − b → + c → if a → = 5.0 i ^ + 4.0 j ^ − 6.0 k ^ , b → = − 2.0 i ^ + 2.0 j ^ + 3.0 k ^ , and c → = 4.0 i ^ + 3.0 j ^ + 2.0 k ^ ? (b) Calculate the angle between r → and the positive z axis. (c) What is the component of a → along the direction of b → ? (d) What is the component of a → perpendicular to the direction of b → but in the plane of a → and b → ? ( Hint: For (c), see Eq. 3-20 and Fig. 3-18; for (d), see Eq. 3-24.)
(a) In unit-vector notation, what is
r
→
=
a
→
−
b
→
+
c
→
if
a
→
= 5.0
i
^
+ 4.0
j
^
− 6.0
k
^
,
b
→
= −2.0
i
^
+ 2.0
j
^
+ 3.0
k
^
, and
c
→
= 4.0
i
^
+ 3.0
j
^
+ 2.0
k
^
? (b) Calculate the angle between
r
→
and the positive z axis. (c) What is the component of
a
→
along the direction of
b
→
? (d) What is the component of
a
→
perpendicular to the direction of
b
→
but in the plane of
a
→
and
b
→
? (Hint: For (c), see Eq. 3-20 and Fig. 3-18; for (d), see Eq. 3-24.)
Use the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.
I need help with this problem:
Two vectors A⃗ A→ and B⃗ B→ are at right angles to each other. The magnitude of A⃗ A→ is 2.00. What should be the length of B⃗ B→ so that the magnitude of their vector sum is 4.00?
Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }.
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.