In: Physics
?⃗ = (2?)?̂− (3?)?̂
?⃗⃗ = (1?)?̂− (2?)?̂
Find
a) ?⃗ − 2?⃗⃗
b) ?⃗ ∙ ?⃗⃗
c) ?⃗ × ?⃗⃗
d) Angle between ?⃗ and ?⃗⃗
Here,
are the unit vectors along the x- and y-axis respectively. The
unit vector along z-axis is denoted by,
.
Subpart a:
Now,
Subpart b:
Here, we have used that
, and
.
Subpart c:
Here, we used that
and
.
Subpart d:
Let the angle between
be
. Then From the rule of dot product we can write,
.
...............(1)
Here,
are the magnitudes of
respectively.
Magnitudes of
can be found in the following way,
and
.
So,
So, the angle, from eqn.....(1).
(Here, we put the result of subpart (b) at the expression of the
dot product of the two vectors,
)
So,
The angle between
is 7.125 degrees.
If this helps, kindly rate the answer. Thanks.