Find the modulus direction cosin unit (1)4a-2b+3c (2)a-7b+5c (3)4a-3b+c
To find the modulus (also known as the magnitude or length) of a vector, as well as its direction cosines, you can follow these steps:
Step 1: Compute the dot product of the vector with itself.
- Let's consider the first vector (1) 4a - 2b + 3c:
- Multiply each component by itself: (4a)^2 + (-2b)^2 + (3c)^2
- Now, let's consider the second vector (2) a - 7b + 5c:
- Multiply each component by itself: (a)^2 + (-7b)^2 + (5c)^2
- Finally, for the third vector (3) 4a - 3b + c:
- Multiply each component by itself: (4a)^2 + (-3b)^2 + (c)^2
Step 2: Calculate the square root of each dot product calculated in step 1.
- Compute the square root of each expression you obtained in step 1.
- For example, for (1) the modulus will be sqrt((4a)^2 + (-2b)^2 + (3c)^2).
Step 3: Normalize the vector to find the direction cosines.
- Divide each component of the vector by its modulus obtained in step 2.
- The direction cosines of a vector are the normalized components.
By following these steps, you will be able to find the modulus and the direction cosines for each given vector.