Download App

Algebra of Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Vectors3 Marks
Question
Express $\overrightarrow{\text{AB}}$ in terms of unit vectors $\hat{\text{i}}\text{ and }\hat{\text{j}}$, when the point is:A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
✓

Answer

Here, A = (-6, 3) B = (-2, -5) Position vector of $\text{A}=-6\hat{\text{i}}+3\hat{\text{j}}$ Position vector of $\text{B}=-2\hat{\text{i}}-5\hat{\text{j}}$ $\overrightarrow{\text{AB}}$ = Position vector of B - Position vector of A$=\big(-2\hat{\text{i}}-5\hat{\text{j}}\big)-\big(-6\hat{\text{i}}+3\hat{\text{j}}\big)$
$=-2\hat{\text{i}}-5\hat{\text{j}}+6\hat{\text{i}}-3\hat{\text{j}}$
$\overrightarrow{\text{AB}}=4\hat{\text{i}}-8\hat{\text{j}}$
$\Big|\overrightarrow{\text{AB}}\Big|=\sqrt{(4)^2+(-8)^2}$
$=\sqrt{16+64}$
$=\sqrt{80}$
$=\sqrt{16\times5}$ $=4\sqrt5$$\Big|\overrightarrow{\text{AB}}\Big|=4\sqrt5$
$\overrightarrow{\text{AB}}=4\hat{\text{i}}-8\hat{\text{j}}$

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 "Solve the Following Question.(3 Marks)" from Algebra of Vectors→Algebra of Vectors — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\text{f(x)}=\begin{cases}2\text{x}^2+\text{k},&\text{if }\text{ x}\geq0\\-2\text{x}^2+\text{k},&\text{if }\text{ x}<0\end{cases},$ then what should be the value of k so that f(x) is continuous at x = 0.
→
Let $A = R_0 \times R,$ where $R_0$ denote the set of all non-zero real numbers. $A$ binary operation $'⊙'$ is defined on $A$ as follows:
$(a, b) ⊙ (c, d) = (ac, bc + d)$ for all $(a, b), (c, d) \in R_0 \times R.$
Show that $'⊙'$ is commutative and associative on $A.$
→
Evaluate the following integrals:
$\int\Big(\frac{\text{x}+1}{\text{x}}\Big)(\text{x}+\log\text{x})^2\text{dx}$
→
Find the intervals in which the following functions are increasing or decreasing.
$f(x) = 2x^3- 9x^2 + 12x - 5$
→
Transform $\left[\begin{array}{ccc}1 & 2 & 4 \\ 3 & -1 & 5 \\ 2 & 4 & 6\end{array}\right]$ into an upper triangular matrix by using suitable row transformations
→
Find the direction cosines of the line passing through two points $(-2, 4, -5)$ and $(1, 2, 3).$
→
Write the negations of the following statements :
(a) If diagonals of a parallelogram are perpendicular, then it is a rhombus.
(b) Mangoes are delicious, but expensive.
(c) A person is rich if and only if he is a software engineer.
→
Find the angle between the given planes.
$\vec{\text{r}}\cdot(2\hat{\text{i}}+3\hat{\text{j}}-6\hat{\text{k}})=5$ and $\vec{\text{r}}\cdot(\hat{\text{i}}-2\hat{\text{j}}+2\hat{\text{k}})=9$
→
Solve the following differential equations:$(1-\text{x}^2)\text{dy + xy dx = xy}^2\text{ dx}$
→
If $A (\bar{a})$ and $B (\bar{b})$ be any two points in the space and $R (\bar{r})$ be a point on the line segment $AB$ dividing it internally in the ratio $m: n$ then prove that $\bar{r}=\frac{m \bar{b}+n \bar{a}}{m+n}$
→