Vector Algebra

Step 1: Formula for angle between two vectors The formula for the sine of the angle between two vectors is given by: $%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7B%7C%5Cvec%7Bf%7D%20%5Ctimes%20%5Cvec%7Bg%7D%7C%7D%7B%7C%5Cvec%7Bf%7D%7C%7C%5Cvec%7Bg%7D%7C%7D$
Step 2: Compute cross product magnitude $%7C%5Cvec%7Bf%7D%20%5Ctimes%20%5Cvec%7Bg%7D%7C$ Using determinant method,

%5Cvec%7Bf%7D%20%5Ctimes%20%5Cvec%7Bg%7D%20%3D%20%5Cbegin%7Bvmatrix%7D%20%5Chat%7Bi%7D%20%26%20%5Chat%7Bj%7D%20%26%20%5Chat%7Bk%7D%20%5C%5C%201%20%26%202%20%26%20-3%20%5C%5C%202%20%26%20-3%20%26%20a%20%5Cend%7Bvmatrix%7D

Expanding, $%5Cvec%7Bf%7D%20%5Ctimes%20%5Cvec%7Bg%7D%20%3D%20%5Chat%7Bi%7D%20(2a%20%2B%209)%20-%20%5Chat%7Bj%7D%20(a%20%2B%206)%20%2B%20%5Chat%7Bk%7D%20(-3%20-%204)$ $%3D%20(2a%20%2B%209)%20%5Chat%7Bi%7D%20-%20(a%20%2B%206)%20%5Chat%7Bj%7D%20-%207%5Chat%7Bk%7D$ $%7C%5Cvec%7Bf%7D%20%5Ctimes%20%5Cvec%7Bg%7D%7C%20%3D%20%5Csqrt%7B(2a%2B9)%5E2%20%2B%20(a%2B6)%5E2%20%2B%2049%7D$
Step 3: Solve for $a$ using $%5Csin%20%5Ctheta$ equation Given $%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7B24%7D%7D%7B28%7D$ , solving for $a$ : $7a%5E2%20%2B%2024a%20%3D%2010$ Thus, the correct answer is option (1).

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Vector Algebra

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs