Choose the correct answer from the given four options. The positi… - Vidyadip

Question

Choose the correct answer from the given four options.
The position vector of the point which divides the join of points $2\vec{\text{a}}-3\vec{\text{b}}$ and $\vec{\text{a}}+\vec{\text{b}}$ in the ratio 3 : 1 is:

$\frac{3\vec{\text{a}}-2\vec{\text{b}}}{2}$
$\frac{7\vec{\text{a}}-8\vec{\text{b}}}{4}$
$\frac{3\vec{\text{a}}}{4}$
$\frac{5\vec{\text{a}}}{4}$

✓

Answer

$\frac{5\vec{\text{a}}}{4}$

Solution:
Let the given points be $\text{A}(2\vec{\text{a}}-3\vec{\text{b}})$ and $\text{B}(\vec{\text{a}}+\vec{\text{b}})$
Let C divides AB in ratio 3 : 1
Now the position vector of a point C dividing the line segment joining the points P and Q, whose position vectors are p and q in the ratio m : n internally, is given by $\frac{\text{m}\vec{\text{q}}+\text{n}\vec{\text{p}}}{\text{m}+\text{n}}$
$\therefore$ Position vector $\text{C}=\frac{3(\vec{\text{a}}+\vec{\text{b}})+1(\vec{2\text{a}}-3\vec{\text{b}})}{3+1}$
$\Rightarrow\text{C}=\frac{5\vec{\text{a}}}{4}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The general solution of differential equation is $(y + c)^2= cx$ where ccis an arbitrary constant. The order and degree of the differential equation are respectively:

If $A$ and $B$ are two independent events with $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{4}$, then $P\left(B^{\prime} \mid A\right)$ is equal to

The solution set of the inequation $3 x+5 y<7$ is

The area of circle $x^2+y^2=4$ is

A and B draw two cards each, one after another, from a pack of well-shuffled pack of 52 cards. The probability that all the four cards drawn are of the same suit is

If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =

R
[0, 1]
[0, 1)
[0, 1)

If $\alpha,\beta,\gamma$ are the angle which a half ray makes with the positive directions of the axis then $\sin^2\alpha + \sin^2\beta + \sin^2\gamma =$

1
2
0
-1

Choose the correct answer from given four options in each of the Exercise:
Let $\text{f}(\text{t})=\begin{vmatrix}\cos\text{t}&\text{t}&1\\2\sin\text{t}&\text{t}&2\text{t}\\\sin\text{t}&\text{t}&\text{t}\end{vmatrix} ,$ then $\lim\limits_{\text{t}\rightarrow0}\frac{\text{f(t)}}{\text{t}^2}$ is equal to:

0
-1
2
3

The area bounded by the curve $x^2 = 4y + 4$ and line $3x + 4y = 0$ is$:$

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+5\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}-4\hat{\text{j}}+5\hat{\text{k}}$ and $\vec{\text{c}}=5\hat{\text{i}}-3\hat{\text{j}}-2\hat{\text{k}},$ then the volume of the parallelopiped with contermious edges $\vec{\text{a}}+\vec{\text{b}},\vec{\text{b}}+\vec{\text{c}},\vec{\text{c}}+\vec{\text{a}}$ is:

2
1
-1
0