If A B C D is a rhombus, whose diagonals intersect at E, then E A… - Vidyadip

MCQ

If $A B C D$ is a rhombus, whose diagonals intersect at $E$, then $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$ equals

✓
$\overrightarrow{0}$
B
$\overrightarrow{A D}$
C
$2 \overrightarrow{B C}$
D
$2 \overrightarrow{A D}$

✓

Answer

Correct option: A.

$\overrightarrow{0}$

(a) : $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$
$
=\overrightarrow{E A}+\overrightarrow{E B}-\overrightarrow{E A}-\overrightarrow{E B}
$ [As diagonals of a rhombus bisect each other]
$=\overrightarrow{0}$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is:

$\int {\frac{{xdx}}{{\sqrt {1 + {x^2} + \sqrt {{{\left( {1 + {x^2}} \right)}^3}} } }}} $ is equal to (where $C$ denotes constant of integration)

Choose the correct answer from the given four options.Corner points of the feasible region determined by the system of linear constraints are $(0, 3), (1, 1)$ and $(3, 0).$ Let $Z = px + qy,$ where $p, q > 0.$ Condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3, 0)$ and $(1, 1)$ is:

If $A = \left[ {\begin{array}{*{20}{c}}1&0\\1&1\end{array}} \right]$ and $I = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$, then which one of the following holds for all $n \ge 1$, (by the principal of mathematical induction)

Solve system of linear equations, using matrix method. $5 x+2 y=4$ ; $7 x+3 y=5$

The restriction on $n, k$ and $p$ so that $PY + WY$ will be defined are:

Given that for each $a \in(0,1)$

$\lim _{n \rightarrow 0^{+}} \int_n^{1-n} t^{-3}(1-t)^{a-1} d t$

exists. Let this limit be $g(a)$. In addition, it is given that the function $g(a)$ is differentiable on $(0,1)$.

$1.$ The value of $g\left(\frac{1}{2}\right)$ is

$(A)$ $\pi$ $(B)$ $2 \pi$ $(C)$ $\frac{\pi}{2}$ $(D)$ $\frac{\pi}{4}$

$2.$ The value of $g ^{\prime}\left(\frac{1}{2}\right)$ is

$(A)$ $\frac{\pi}{2}$ $(B)$ $\pi$ $(C)$ $-\frac{\pi}{2}$ $(D)$ $0$

Give the answer question $1$ and $2.$

Given that $A$ is a square matrix of order $3$ and $|A| = -4,$ then $|\operatorname{ad}| A \mid$ is equal to :

The system of equation x + y + z = 2, 3x − y + 2z = 6 and 3x + y + z = −18 has:

The altitude of a cone is $20\ cm$ and its semi $-$ vertical angle is $30^\circ .$ If the semi $-$ vertical angle is increasing at the rate of $2^\circ $ per second, then the radius of the base is increasing at the rate of :