Maths-

General

Easy

Question

# Let and A vector is such that

Hint:

### There are four vectors. We are given three of the vectors. We have to find the fourth vector. We are given the dot product of fourth vector with each of the three vectors. We will assume variables for the components of the fourth vector. Then, we will find the dot product.

## The correct answer is:

### The three vectors are as follows:

Let the fourth vector be

We will write the dot products now:

We will take the dot products of the given vectors with .

Now we have three simultaneous equations. We will solve them to get final answer.

Step 1: Add the three equation.

2x + 3y + z = 9

+ 4x + y = 7

+ x - 3y - 7z = 6

_________________________________

7x + y - 6z = 22 ...(4)

Step 2: Subtract (2) from (4)

7x + y - 6z = 22

- _{(-)}4x +_{(-)} y = 7

_________________________________

3x - 6z = 15

Divide both the sides by 3.

x - 2z = 5 ...(5)

Step 3: Multiply equation (1) by 2 and add equation (5) to it.

2(2x + 3y + z) = 2(9)

4x + 6y + 2z = 18

+ x + 0 - 2z = 5

______________________________

5x + 6y = 23 ...(6)

Step 4: Multiply equation (2) by -6 and add (6) and (2)

-6(4x + y) = -6(7)

-24x - 6y = -42

+ 5x + 6y = 23

__________________________________

-19x + 0 = -19

x = 1

Step 5: Substituting value of x in equation (2) and (5)

4(1) + y = 7

y = 3

(1) -2z = 5

-2z = 4

z = -2

Substituting the values of x,y and z we get

This is the final answer.

We can solve simultaneous equations as we feel easy for us. There are not any particular steps to be followed. We just have to solve the equation to find the values of the variables. We try to eliminate the variables using addition and subtraction to single out single variable.

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