Advertisements
Advertisements
प्रश्न
Find the sum of the vectors `veca = hati -2hatj + hatk, vecb = -2hati + 4hatj + 5hatk and vecc = hati - 6hatj - 7hatk.`
उत्तर
`veca = hati -2hatj + hatk, vecb = -2hati + 4hatj + 5hatk` and `vecc = hati - 6hatj - 7hatk`
sum total
`veca + vecb + vecc` = `(1 - 2 + 1)hati + (-2 + 4 - 6)hatj + (1 + 5 - 7)hatk`
= `0.hati - 4.hatj - 1.hatk`
= `-4hatj - hatk`
APPEARS IN
संबंधित प्रश्न
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 = vecb + vecc`, then is it true that `|veca| = |vecb| + |vecc|`? Justify your answer.
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
\[\overrightarrow{AB} + \overrightarrow{AE} + \overrightarrow{BC} + \overrightarrow{DC} + \overrightarrow{ED} + \overrightarrow{AC} = 3\overrightarrow{AC}\]
Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.
If P is a point and ABCD is a quadrilateral and \[\overrightarrow{AP} + \overrightarrow{PB} + \overrightarrow{PD} = \overrightarrow{PC}\], show that ABCD is a parallelogram.
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.
Prove that the points \[\hat{i} - \hat{j} , 4 \hat{i} + 3 \hat{j} + \hat{k} \text{ and }2 \hat{i} - 4 \hat{j} + 5 \hat{k}\] are the vertices of a right-angled triangle.
Find the sum of the following vectors: \[\overrightarrow{a} = \hat{i} - 2 \hat{j} , \overrightarrow{b} = 2 \hat{i} - 3 \hat{j} , \overrightarrow{c} = 2 \hat{i} + 3 \hat{k} .\]
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 ______
`[(bar"a", bar"b" + bar"c", bar"a" + bar"b" + bar"c")]` = ______.
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 ______.
`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 ______.
ABCD is a rhombus whose diagonals intersect at E . Then `vec(EA) + vec(EB) + vec(EC) + vec(ED)` equals to ______.
