मराठी

If a=xi+2j−zk and b=3i−yj+k are two equal vectors ,then write the value of x+y+z - Mathematics

Advertisements
Advertisements

प्रश्न

If `veca=xhati+2hatj-zhatk and vecb=3hati-yhatj+hatk` are two equal vectors ,then write the value of x+y+z

उत्तर

Given `veca=xhati+2hatj-zhatk and vecb=3hati-yhatj+hatk` are two equal vectors 

`therefore xhati+2hatj-zhatk=3hati-yhatj+hatk`

x=3,y=-2,z=-1

x+y+z=3+(-2)+(-1)=0

Therefore, the value of x + y + z is 0.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2012-2013 (March) Delhi Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

If \[\vec{a}\] and \[\vec{b}\] are two non-collinear vectors such that \[x \vec{a} + y \vec{b} = \vec{0} ,\] then write the values of x and y.


If \[\overrightarrow{a} = \hat{i} + \hat{j} , \overrightarrow{b} = \hat{j} + \hat{k} , \overrightarrow{c} = \hat{k} + \hat{i}\], find the unit vector in the direction of \[\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}\].


If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] and \[\vec{d}\] are the position vectors of points A, B, C, D such that no three of them are collinear and \[\vec{a} + \vec{c} = \vec{b} + \vec{d} ,\] then ABCD is a


If ABCDEF is a regular hexagon, then \[\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}\] equals

 


Find the components along the coordinate axes of the position vector of the following point :

Q(–5, 1)


In the given figure express `bar"c"` and `bar"d"` in terms of `bar"a"` and `bar"b"`.


Select the correct option from the given alternatives:

If `bar"a"  "and"  bar"b"` are unit vectors, then what is the angle between `bar"a"` and `bar"b"` for `sqrt3bar"a" - bar"b"` to be a unit vector?


Select the correct option from the given alternatives:

The value of `hat"i".(hat"j" xx hat"k") + hat"j".(hat"i" xx hat"k") + hat"k".(hat"i" xx hat"j")` is


In a parallelogram ABCD, diagonal vectors are `bar"AC" = 2hat"i" + 3hat"j" + 4hat"k" and bar"BD" = - 6hat"i" + 7hat"j" - 2hat"k"`, then find the adjacent side vectors `bar"AB" and bar"AD"`.


If `|bar"a"| = |bar"b"| = 1,  bar"a".bar"b" = 0, bar"a" + bar"b" + bar"c" = bar"0", "find"  |bar"c"|`.


Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2, 4).


ABCD is a parallelogram. E, F are the midpoints of BC and CD respectively. AE, AF meet the diagonal BD at Q and P respectively. Show that P and Q trisect DB.


Find a unit vector perpendicular to the plane containing the point (a, 0, 0), (0, b, 0) and (0, 0, c). What is the area of the triangle with these vertices?


State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:

`|bar"a"|. (bar"b" + bar"c")`


a and b are non-collinear vectors. If c = (x - 2)a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = ______.


If `vec"a" = 2hat"i" - hat"j" + hat"k", vec"b" = hat"i" + hat"j" - 2hat"k"` and `vec"c" = hat"i" + 3hat"j" - hat"k"`, find `lambda` such that `vec"a"` is perpendicular to `lambdavec"b" + vec"c"`.


The unit vector perpendicular to the vectors `hat"i" - hat"j"` and `hat"i" + hat"j"` forming a right handed system is ______.


If `vec"a" = hat"i" + hat"j" + 2hat"k"` and `hat"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `2vec"a" - vec"b"`


If `vec"a"` is any non-zero vector, then `(vec"a" .hat"i")hat"i" + (vec"a".hat"j")hat"j" + (vec"a".hat"k")hat"k"` equals ______.


The formula `(vec"a" + vec"b")^2 = vec"a"^2 + vec"b"^2 + 2vec"a" xx vec"b"` is valid for non-zero vectors `vec"a"` and `vec"b"`


Classify the following measures as scalar and vector.

10-19 coulomb


Classify the following as scalar and vector quantity.

Force


If `veca` and `vecb` are two collinear vectors then which of the following are incorrect.


If `veca = hati - hatj + 7hatk` and `vecb = 5hati - hatj + λhatk`, then find the value of λ so that the vectors `veca + vecb` and `veca - vecb` are orthogonal.


Check whether the vectors `2hati + 2hatj + 3hat k, -3hati + 3hatj + 2hat k` and `3hati + 4hatk` form a triangle or not.


If A(1, 2, – 3) and B(– 1, – 2, 1) are the end points of a vector `vec("AB")` then find the unit vector in the direction of `vec("AB")`.


Check whether the vectors `2hati+2hatj+3hatk,-3hati+3hatj+2hatk` and `3hati+4hatk` form a triangle or not.


Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.


In the triangle PQR, `bar(PQ) = 2bara and bar(QR) = 2barb`. The mid-point of PR is M. Find the following vectors in terms of `bara and barb`.  

  1. `bar(PR)`
  2. `bar(PM)`
  3. `bar(QM)`

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×