Out of the following vectors, identify the one which is normal to the force, F = 4 i - 3 j .

Step-by-step solution

Two vectors are normal to each other if their dot product is zero. Given force vector F = 4 i - 3 j . Checking the dot product of F with each of the given vectors: For option (1): (4 i - 3 j ) (-6 i ) = (4)(-6) + (-3)(0) = -24 0 For option (2): (4 i - 3 j ) (7 i ) = (4)(7) + (-3)(0) = 28 0 For option (3): (4 i - 3 j ) (3 i + 4 j ) = (4)(3) + (-3)(4) = 12 - 12 = 0 For option (4): (4 i - 3 j ) (4 i + 3 j ) = (4)(4) + (-3)(3) = 16 - 9 = 7 0 Since the dot product is zero for the vector 3 i + 4 j , it is normal to the g