Question

?⃗ = (2?)?̂− (3?)?̂
?⃗⃗ = (1?)?̂− (2?)?̂

Find
a) ?⃗ − 2?⃗⃗
b) ?⃗ ∙ ?⃗⃗
c) ?⃗ × ?⃗⃗
d) Angle between ?⃗ and ?⃗⃗

Answer 1

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.

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