Question

calculate the values of (i) j.(2i - 3j+k)
(ii) (2i - j ). (3i+ k)

Answer 1

I hope this will help you
if not then comment me

Answer 2

Given,

(i) j.(2i - 3j+k)

(ii) (2i - j ).(3i+ k)

To find,

The values of the respective dot products.

Solution,

We can simply solve this numerical problem by using the following process:

As per the principles of vectors dot multiplication,

The dot product any of two unit vectors is as follows-

a) i.i = j.j = k.k = 1

b) i.j = j.i = j.k = k.j =k.i = i.k = 0

Now, according to the question;

(i) j.(2i - 3j+k)

= (j).(2i) - (j).(3j) + (j).(k)

= 2×(j).(i) - 3×(j).(j) + (j).(k)

= 2×0 - 3×1 + 0

= (-3)

(ii) (2i - j ).(3i+ k)

= (2i).(3i+ k) - (j).(3i+ k)

= (2i).(3i) + (2i).(k) - (j).(3i) - (j).(k)

= 6×(i).(i) + 2×(i).(k) - 3×(j).(i) - (j).(k)

= 6×1 + 2×0 - 3×0 - 0

= (+6)

Hence, the values of the respective dot products are (-3) and (+6), respectively.