Question

What is the value of m if i + mj + k is a unit vector.

Answer 1

i + mj + k

Resultant of vector is
1 = sqrt(1^2 + m^2 + 1^2)
1 - 2 = m^2
-1 = m^2
m = sqrt(-1) = i

m is an imaginary unit.

Answer 2

Answer:

The value of m for the given unit vector is  ± $\frac{1}{\sqrt{2} }$

Explanation:

Given: The given unit vector  i + mj + k

To find: The value of m for the given unit vector.

Solution:

Unit vector:

• A vector with a magnitude of one is referred to as a unit vector.

• Unit vectors are denoted by the "cap" sign .
• The length of a unit vector is one. It is frequently used to describe the direction of a vector.

The formula for magnitude of any vector(ai + bj + ck) is $\sqrt{a^{2} +b^{2} +c^{2} }$

The given unit vector is (i + mj + k)

The magnitude is given by $\sqrt{1^{2} + m^{2} + 1^{2} }$

               ⇒ $\sqrt{2 +m^{2} }$

 ⇒ $\sqrt{2 +m^{2} }$ = 1

 ⇒|m|$\sqrt{2} = 1$

In this |m| represents the absolute value of m.

If m is negative, we take the additive inverse of it.

But in the given condition m value is the positive one. so we can take the original value.

⇒|m| = 1 ÷ √2

m = $\frac{1}{\sqrt{2} }$

m = ± $\frac{1}{\sqrt{2} }$

Final answer:

The value of m for the given unit vector is  ± $\frac{1}{\sqrt{2} }$

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