MyQuestionIcon

11

You visited us 11 times! Enjoying our articles? Unlock Full Access!

Order of Magnitude

Three force v...

Question

Three force vectors $\to P, \to Q, \to R$ of 15kg. each act along AB, BC and CA respectively. The position vectors of $A, B$ and $C$ are given by $\to O A = 2 i - 4 j + 3 k$ , $\to O B = 5 i + 3 j - 2 k,$ $\to O C = - 2 i + 2 j + 3 k .$ Find the resultant force vector $\to S$ of the vectors $\to P, \to Q$ and $\to R .$

A

= 15 [\frac{3 i + 7 j + 5 k}{\sqrt{(83)}} + \frac{7 i - j + 5 k}{5 \sqrt{(3)}} + \frac{4 i - 6 j}{2 \sqrt{(13)}}]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

= 15 [\frac{3 i - 7 j - 5 k}{\sqrt{(83)}} + \frac{- 7 i - j - 5 k}{5 \sqrt{(3)}} + \frac{4 i + 6 j}{2 \sqrt{(13)}}]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

= 15 [\frac{3 i + 7 j - 5 k}{\sqrt{(83)}} + \frac{- 7 i - j + 5 k}{5 \sqrt{(3)}} + \frac{4 i - 6 j}{2 \sqrt{(13)}}]

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

= 15 [\frac{3 i + 7 j + 5 k}{\sqrt{(83)}} + \frac{7 i + j + 5 k}{5 \sqrt{(3)}} + \frac{4 i + 6 j}{2 \sqrt{(13)}}]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $= 15 [\frac{3 i + 7 j - 5 k}{\sqrt{(83)}} + \frac{- 7 i - j + 5 k}{5 \sqrt{(3)}} + \frac{4 i - 6 j}{2 \sqrt{(13)}}]$
$\to A B = \to O B - \to O A$
$= (5 i + 3 j - 2 k) - (2 i - 4 j + 3 k) = 3 i + 7 j - 5 k$
$\to B C = \to O C - \to O B$
$= (- 2 i + 2 j + 3 k) - (5 i + 3 j - 2 k) = - 7 i - j + 5 k$

$\to C A = \to O A - \to O C$
$= (- 2 i - 4 j + 3 k) - (- 2 i + 2 j + 3 k) = 4 i - 6 j$

$∴ \to S = \to P + \to Q + \to R = 15 ⎡ ⎢ ⎣ \frac{\to A B}{∣ ∣ \to A B ∣ ∣} + \frac{\to B C}{∣ ∣ \to B C ∣ ∣} + \frac{\to C A}{∣ ∣ \to C A ∣ ∣} ⎤ ⎥ ⎦$

$= 15 [\frac{3 i + 7 j - 5 k}{\sqrt{(83)}} + \frac{- 7 i - j + 5 k}{5 \sqrt{(3)}} + \frac{4 i - 6 j}{2 \sqrt{(13)}}]$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Show the each of the following triads of vectors are coplanar:
(i)

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

Q. The perimeter of a triangle with sides

3 i + 4 j + 5 k, 4 i - 3 j - 5 k

7 i + j

Q. Find the volume of a parallelopiped whose sides are given by

- 3 ˆ i + 7 ˆ j + 5 ˆ k, - 5 ˆ i + 7 ˆ j - 3 ˆ k

7 ˆ i - 5 ˆ j - 3 ˆ k

Q. The points whose position vectors are

5 ˆ i + 5 ˆ k, 2 ˆ i + ˆ j + 3 ˆ k

- 4 ˆ i + 3 ˆ j - ˆ k

The position vectors of three particles are (i + 2j + 3k), (5i - 2j + 2k) and (3i - 6j + 4k) and their masses are respectively 2 kg, 1 kg and 3 kg. The position vector of a fourth mass of 4 kg, so that the centre of mass of the system may be at the origin, is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Significant Figures

PHYSICS

Watch in App

explore_more_icon

Explore more

Order of Magnitude

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon