Question

# The vectors are equal in length and pair wise make equal angles. If , then

Hint:

### We are given three vectors of same length. The angle between the pairs of the vector is same too. We are given the two vectors. We have to find the remaining vector. We will assume the variables for the remaining vector. We will use it for all the given conditions. Then, we will find the values of the variable hence the vector.

## The correct answer is:

### The given vectors are .

All the three vectors are of equal lengths.

...(1)

So, the length of all the vectors will be √2

Let the angle between each pair from the given vectors be A.

Let's write the dot product of each pair.

The next pair will be

Now we will solve the equation

y + z = 1 ...(3)

x + y = 1 ...(4)

Subtracting (4) from (3)

z - x = 0

x = z

Now, we know that length of all vectors is √2

We will rearrange equation (3) and substitute in the above equation.

y + z = 1

y = 1 - z

If we see the options, we don't have the value of z component as fraction. So, we will just focus on the value of z = 1

y = 1 - z

y = 1 - 1

y = 0

x + y = 1

x + 0 = 1

x = 1

The solution is (1,0,1).

For such questions, concept of scalar product is important. When we take a dot product of two vectors, we get a scalar value. This is called as scalar product.

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