Maths · Vectors and scalars, the addition of vectors
Three vectors and are as shown in figure. If magnitude of is and then the magnit
Three vectors \( \vec{A}, \vec{B} \) and \( \vec{C} \) are as shown in figure. If magnitude of \( \vec{A} \) is \( 4 \mathrm{m} \) and \( \vec{A}+\vec{B}+\vec{C}=0, \) then the magnitude of \( \vec{B} \) and \( \vec{C} \) are respectively
- A. \( 4 m, 4 m \)
- B. \( 4 \sqrt{3} m, 4 \sqrt{3} m \)
- C. \( 4 m, 4 \sqrt{3} m \)
- D. \( 4 \sqrt{3} m, 4 m \)
Step-by-step solution
Given A + B + C = 0, the vectors form a closed triangle. With |A| = 4 m, and from the typical figure (B at 0°, C at 150°), resolving components gives B = 4√3 m and C = 4 m, satisfying the condition.
Related MCQs
- The vector bisects the angles between the vectors and if…
- Any vector in an arbitrary direction can always be replaced by two (or three)…
- Let be a triangle and let be its circumcentre and be its orthocentre. The…
- A zero vector has…
- If and are non-collinear vectors and \boldsymbol{a}+(\boldsymbol{2} \boldsymbol{p}+\boldsymbol{q}+\mathbf{1}) \boldsymbol{b} \) \boldsymbol{…