Question

If a=ai and b=bj then a.b is equal to

Answer 1

Answer:

The value of a.b = 0.

Step-by-step explanation:

Given:

a = ai and b = bj

To find:

The value of a.b

Step 1

Let a = ai and b = bj

Here a = ai

Subtract ai from both sides, of the above equation, then we get

a - ai = ai - ai

Simplifying the equation,

a - ai = 0

Factor a - ai:

a - ai = 0

(1 - i)a = 0

Step 2

Using the Zero Factor Principle:

If a.b = 0 then a = 0 or b = 0

a = 0

Step 3

Similarly

b = bj

Subtract bj from both sides, of the above equation, then we get

b - bj = bj - bj

Simplify

b - bj = 0

Factor b - bj:

b - bj  = 0

(1 - j)b = 0

Therefore, the value of a.b = 0.

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Answer 2

Answer:

a.b is equal to 0.

Step-by-step explanation:

As per the question,

We need to find out the dot product of a i and b j

As we know,

• Dot product of any two vectors is the multiplication of the constants with cos of the angle between the vectors.
• Since, here the vectors are in i direction = x axis and j direction = y axis.
• So, it has 90 degree angle.

Now,

$a.b= ab\:cos(90\°)\\a.b = 0 \\as\: cos90\°=0$

Hence, a.b is equal to 0.

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