Question

ki+1/2j is a unit vector then k can be equal to
(a) √3/2
(b) 1/2
(c) 1
(d) 2​

Answer 1

Answer:

1

Explanation:

• a unit is a vector that has a magnitude of 1. they are labelled with a '' '' , for example any vector can become a unit vector by dividing it by the vector's magnitude. Vectors are often written in xyz coordinates.

Answer 2

The correct option is a, i.e., √3/2.

Given:

ki+1/2j is a unit vector.

To find:

The value of k.

Solution:

• A vector is a quantity which has both direction and magnitude which is represented in the form of ai+bj+ck=0 where i denotes the direction towards x axis, j denotes the direction towards y axis and k denotes the direction towards z axis.
• Magnitude is the length of a vector and we can find the magnitude of a vector by using the formula:
• |A|= $\sqrt{a^{2}+b^{2} +c^{2} }$    (For A= ai+bj+ck=0 )
• Unit vector is a type of vector whose magnitude is one.

Let V= ki+1/2j

Since, V is an unit vector (given).

So, magnitude of V= |V|= 1

|V|= $\sqrt{k^{2} +( \frac{1}{2})^{2} }$               (Using the above formula)

|V|= $\sqrt{k^{2} + \frac{1}{4} }$

1= $\sqrt{k^{2} + \frac{1}{4} }$

On squaring both the sides we get,

1= $k^{2} + \frac{1}{4}$

k²= 1- $\frac{1}{4}$

k²= $\frac{3}{4}$

k= √3/2

So, the value of k is √3/2.

Therefore, the correct option is a, i.e., √3/2.

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