Find the modulus direction cosin unit vector 1)4a-2b+3c, 2)a-7b+5c, 3)4a-3b+c.
To find the modulus (or magnitude) of a vector, you need to calculate the square root of the sum of the squares of its components. In this case, we have three vectors represented by their components as follows:
1) Vector 1: 4a - 2b + 3c
2) Vector 2: a - 7b + 5c
3) Vector 3: 4a - 3b + c
To find the modulus for each of these vectors, you can use the following formula:
||v|| = √(a^2 + b^2 + c^2)
Let's calculate the modulus for each vector one by one:
1) Modulus of Vector 1:
||v1|| = √((4a)^2 + (-2b)^2 + (3c)^2)
= √(16a^2 + 4b^2 + 9c^2)
2) Modulus of Vector 2:
||v2|| = √((a)^2 + (-7b)^2 + (5c)^2)
= √(a^2 + 49b^2 + 25c^2)
3) Modulus of Vector 3:
||v3|| = √((4a)^2 + (-3b)^2 + (c)^2)
= √(16a^2 + 9b^2 + c^2)
Now you have the modulus of each vector based on their components.