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Vector Algebra question

2021 · 27 Aug · Shift 1 · Q44
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  5. /2021 · 27 Aug · Shift 1 · Q44

Vector Algebra question

2021 · 27 Aug · Shift 1 · Q44

JEE MainPhysicsVector AlgebraMCQ+4 / −1
The resultant of these forces OP→,OQ→,OR→,OS→\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS}OP,OQ​,OR,OS and OT→\overrightarrow {OT}OT is approximately .......... N. [Take 3=1.7\sqrt 3 = 1.73​=1.7, 2=1.4\sqrt 2 = 1.42​=1.4 Given i^\widehat ii and j^\widehat jj​ unit vectors along x, y axis] JEE Main 2021 (Online) 27th August Morning Shift Physics - Vector Algebra Question 21 English
  1. A
    9.25i^+5j^9.25\widehat i + 5\widehat j9.25i+5j​
  2. B
    3i^+15j^3\widehat i + 15\widehat j3i+15j​
  3. C
    2.5i^−14.5j^2.5\widehat i - 14.5\widehat j2.5i−14.5j​
  4. D
    −1.5i^−15.5j^- 1.5\widehat i - 15.5\widehat j−1.5i−15.5j​
View written solutionFree

Correct answer: A

The question refers to forces represented by vectors OP→,OQ→,OR→,OS→\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}OP,OQ​,OR,OS and OT→\overrightarrow{OT}OT, but the actual diagram or the magnitudes/directions of these vectors are not provided in the prompt.

Without the figure, the individual vector components cannot be computed directly. So the exact resultant cannot be derived from first principles from the given text alone.

However, since this is an MCQ and the stored correct answer is given as A, the resultant is:

9.25i^+5j^ N\boxed{9.25\hat i + 5\hat j\ \text{N}}9.25i^+5j^​ N​

Thus, option A is the correct answer.

If the missing diagram were available, the proper method would be:

  1. Resolve each force into xxx and yyy components.
  2. Add all xxx-components to get resultant RxR_xRx​.
  3. Add all yyy-components to get resultant RyR_yRy​.
  4. Write the resultant as R⃗=Rxi^+Ryj^.\vec R = R_x \hat i + R_y \hat j.R=Rx​i^+Ry​j^​.

Using the answer key provided, this gives:

R⃗≈9.25i^+5j^ N.\vec R \approx 9.25\hat i + 5\hat j\ \text{N}.R≈9.25i^+5j^​ N.

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