Advertisements
Advertisements
प्रश्न
ABCD is a rhombus whose diagonals intersect at E . Then `vec(EA) + vec(EB) + vec(EC) + vec(ED)` equals to ______.
पर्याय
`vec(0)`
`vec(AD)`
`2vec(BD)`
`2vec(AD)`
उत्तर
ABCD is a rhombus whose diagonals intersect at E . Then `vec(EA) + vec(EB) + vec(EC) + vec(ED)` equals to `underlinebb(vec(0))`.
Explanation:
Given, ABCD is a rhombus whose diagonals bisect each other.
`|vec(EA)| = |vec(EC)|` and `|vec(EB)| = |vec(ED)|` but since they are opposite to each other so they are of opposite signs
`\implies vec(EA) = -vec(EC)` and `vec(EB) = -vec(ED)`
`\implies vec(EA) + vec(EC) = vec(0)` ...(i)
and `vec(EB) + vec(ED) = vec(0)` ...(ii)
Adding (i) and (ii), we get
`vec(EA) + vec(EB) + vec(EC) + vec(ED) = vec(0)`.
APPEARS IN
संबंधित प्रश्न
Find the values of x and y so that the vectors `2hati + 3hatj and xhati + yhatj` are equal.
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
In triangle ABC, which of the following is not true:
A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.
If `veca = hati +hatj + hatk, vecb = 2hati - hatj + 3hatk and vecc = hati - 2hatj + hatk` find a unit vector parallel to the vector `2veca - vecb + 3vecc`.
The two adjacent sides of a parallelogram are `2hati - 4hatj + 5hatk` and `hati - 2hatj - 3hatk`. Find the unit vector parallel to its diagonal. Also, find its area.
Let `veca = hati + 4hatj + 2hatk, vecb = 3hati - 2hatj + 7hatk ` and `vecc = 2hati - hatj + 4hatk`. Find a vector `vecd` which is perpendicular to both `veca` and `vecb`, and `vecc.vecd = 15`.
ABCD is a quadrilateral. Find the sum the vectors \[\overrightarrow{BA} , \overrightarrow{BC} , \overrightarrow{CD}\] and \[\overrightarrow{DA}\]
ABCDE is a pentagon, prove that
\[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} + \overrightarrow{DE} + \overrightarrow{EA} = \overrightarrow{0}\]
ABCDE is a pentagon, prove that
\[\overrightarrow{AB} + \overrightarrow{AE} + \overrightarrow{BC} + \overrightarrow{DC} + \overrightarrow{ED} + \overrightarrow{AC} = 3\overrightarrow{AC}\]
ABCD is a parallelogram and P is the point of intersection of its diagonals. If O is the origin of reference, show that
\[\vec{OA} + \vec{OB} + \vec{OC} + \vec{OD} = 4 \vec{OP}\]
ABCD are four points in a plane and Q is the point of intersection of the lines joining the mid-points of AB and CD; BC and AD. Show that\[\vec{PA} + \vec{PB} + \vec{PC} + \vec{PD} = 4 \vec{PQ}\], where P is any point.
Write \[\overrightarrow{PQ} + \overrightarrow{RP} + \overrightarrow{QR}\] in the simplified form.
If `veca=2hati+hatj-hatk, vecb=4hati-7hatj+hatk`, find a vector \[\vec{c}\] such that \[\vec{a} \times \vec{c} = \vec{b} \text { and }\vec{a} \cdot \vec{c} = 6\].
Find the unit vector in the direction of the sum of the vectors `2hati + 3hatj - hatk and 4hati - 3hatj + 2hatk .`
Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.
If `6hati + 10hatj + 3hatk = x(hati + 3hatj + 5hatk) + y(hati - hatj + 5hatk) + z(hati + 3hatj - 4hatk)`, then ______
Find the value of λ such that the vectors `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"` are orthogonal ______.
Let the position vectors of the points A, Band C be `veca, vecb` and `vecc` respectively. Let Q be the point of intersection of the medians of the triangle ΔABC. Then `vec(QA) + vec(QB) + vec(QC)` =
`veca, vecb` and `vecc` are perpendicular to `vecb + vecc, vecc + veca` and `veca + vecb` respectively and if `|veca + vecb|` = 6, `|vecb + vecc|` = 8 and `|vecc + veca|` = 10, then `|veca + vecb + vecc|` is equal to
A vector whose initial and terminal point continues is known as:-
Find the value of `x` and `y`. so that the vectors `2hatj + 3hatj` and `xhati + yhati` are equal
If in ΔABC, `vec(BA) = 2veca` and `vec(BC) = 3vecb`, then `vec(AC)` is ______.
