Question

Let, →a and →c are unit vectors and ∣∣∣→b∣∣∣=4. The angle between →a and →c is cos−1(14). If →b−2→c=λ→a, then λ is equal to

A. 3,4
B. -3,4
C. 3,-4
D. 1/4,3/4

Answer 1

To find the value of λ, we can solve the given equation for λ. We are given that →b - 2→c = λ→a. Since →a and →c are unit vectors, their magnitudes are 1.

Therefore, the magnitude of →a is 1. Also, we are given that |→b| = 4. This means the magnitude of →b is 4. Now, let's substitute these values into the equation. Therefore, λ is equal to 2. So, none of the given options are correct.

Step-by-step explanation:

To find the value of λ, we can solve the given equation for λ. We are given that →b - 2→c = λ→a. Since →a and →c are unit vectors, their magnitudes are 1. Therefore, the magnitude of →a is 1. Also, we are given that |→b| = 4. This means the magnitude of →b is 4. Now, let's substitute these values into the equation:

|→b - 2→c| = λ

|4 - 2→c| = λ

Since →c is a unit vector, its magnitude is 1. Therefore, we have:

|4 - 2(1)| = λ

|4 - 2| = λ

|4 - 2| = λ

|2| = λ

2 = λ

Therefore, λ is equal to 2. So, none of the options given (A. 3,4 B. -3,4 C. 3,-4 D. 1/4,3/4) are correct.