Find the angle between two vectors A =5i +j B= 2i+4j helpppp!!!
Answers
Answered by
4
Answer:
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solution:
Explanation:
We're asked to find the angle between two vectors, given their unit vector notations.
To do this, we can use the equation
→
A
⋅
→
B
=
A
B
cos
θ
rearranging to solve for angle,
θ
:
cos
θ
=
→
A
⋅
→
B
A
B
θ
=
arccos
⎛
⎝
→
A
⋅
→
B
A
B
⎞
⎠
where
→
A
⋅
→
B
is the dot product of the two vectors, which is
→
A
⋅
→
B
=
A
x
B
x
+
A
y
B
y
+
A
z
B
z
....
= (5×2)+(4×1)=10+4=14
A =√5^2+1^2=√26
B =√2^2+4^2=√20
Therefore we have
cos
θ= 14
14/√520
therefore angle between two vectors is 70°36`
Answered by
4
Answer:
A=2i^+3j^−4k^
And B=5i^+2j^+4k^
cosθ=ABA.B
cosθ=22+32+(−4)252+22+42(2i^+3j^−4k^).(5i^+2j^+4k^)
=22+32+(−4)252+22+42(10+6−16)=0
Therefore, cosθ=0
θ=90∘
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