English

Find the sum of the vectors anda→=i^-2j^+k^,b→=-2i^+4j^+5k^andc→=i^-6j^-7k^. - Mathematics

Advertisements
Advertisements

Question

Find the sum of the vectors `veca = hati -2hatj + hatk, vecb = -2hati + 4hatj + 5hatk and vecc = hati - 6hatj - 7hatk.`

Sum

Solution

`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`

shaalaa.com
  Is there an error in this question or solution?
Chapter 10: Vector Algebra - Exercise 10.2 [Page 440]

APPEARS IN

NCERT Mathematics [English] Class 12
Chapter 10 Vector Algebra
Exercise 10.2 | Q 6. | Page 440

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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).


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.


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 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.


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.


Write \[\overrightarrow{PQ} + \overrightarrow{RP} + \overrightarrow{QR}\] in the simplified form.


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 .`


`[(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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×