# Find Scalar 'a' for Perpendicular Vectors L and K | Vector Product Homework

• xphloem
In summary: You should be able to solve that equation for a single value of a.In summary, the problem asks for the value of scalar 'a' that makes the vector L - aK perpendicular to L. Using the dot product, we set (i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0 and solve for a, resulting in a single value of a that satisfies the equation.

## Homework Statement

Consider the two vectors L= i +2j+3K
K=4i+5j+6k
Find scalar 'a' such that:
L - aK is perpndicular to L.

## Homework Equations

if two vectors are perpenicular dot product=0

## The Attempt at a Solution

(i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0
I get three values of a here. but none satisfies th whole equations at the same time. Please help me

I don't understand what you mean by the last line.

Can you show us how you calculated the dot product?
Surely it yields a linear equation in a? How can it possibly result in 3 values for a?
There is only one equation, how can you not be able to find one a that satisfies the whole equation at the same time?

You probably made a mistake with the dot product:

$$(a \hat{i} + b\hat{j} + c\hat{k} ) \cdot ( d\hat{i} + e\hat{j} + f\hat{k}) = ad + be + cf$$

xphloem said:

## The Attempt at a Solution

(i+2j+3k).{(1-4a)i+(2-5a)j+(3-6a)k}=0
I get three values of a here. but none satisfies th whole equations at the same time. Please help me

Complete the dot product you wrote, using Nick89's formula if you didn't know it already. You'll get a linear equation in a.

## 1. What is a scalar?

A scalar is a quantity that has magnitude but no direction. Scalars can be positive or negative and can be measured in units such as time, mass, or temperature.

## 2. What are perpendicular vectors?

Perpendicular vectors are two vectors that intersect at a right angle, forming a 90-degree angle. This means that the dot product of the two vectors is equal to zero.

## 3. How do you find the scalar 'a' for perpendicular vectors L and K?

To find the scalar 'a' for perpendicular vectors L and K, you can use the vector product formula (L x K = a). Plug in the values for the two vectors and solve for 'a' using algebraic manipulation.

## 4. What is the vector product formula?

The vector product formula is (L x K = a), where L and K are two vectors and 'a' is the scalar value that is being solved for. This formula is used to find the scalar value when given two perpendicular vectors.

## 5. Why is finding the scalar 'a' important?

Finding the scalar 'a' is important because it allows us to solve for unknown values in equations involving perpendicular vectors. It is also important in physics and engineering applications, where perpendicular vectors are commonly used to represent forces and motions.