OnlineCBT
Physics · MOTION IN A PLANE
हिन्दीTwo vectors are given as \( \mathbf{A} = 3\hat{\mathbf{i}} - 4\hat{\mathbf{j}} \) and \( \mathbf{B} = \lambda \hat{\mathbf{i}} + 6\hat{\mathbf{j}} \). If vector \( \mathbf{B} \) is anti-parallel to vector \( \mathbf{A} \), determine the value of the scalar \( \lambda \) and the magnitude of vector \( \mathbf{B} \).
Correct answer · Option 1
\( \lambda = -4.5 \), \( |\mathbf{B}| = 7.5\text{ units} \)
Explanation
Anti-parallel implies \( \mathbf{B} = k\mathbf{A} \) with \( k < 0 \). Equating y-components: \( 6 = -4k \implies k = -1.5 \). So \( \lambda = 3k = -4.5 \), and magnitude \( |\mathbf{B}| = 1.5 \times \sqrt{3^2 + (-4)^2} = 7.5\text{ units} \).
