हिंदी

Select the correct option from the given alternatives: If a|a¯|=3 and - 1 ≤ k ≤ 2, then ka|ka¯| lies in the interval - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct option from the given alternatives:

If `|bar"a"| = 3` and - 1 ≤ k ≤ 2, then `|"k"bar"a"|` lies in the interval

विकल्प

  • [0, 6]

  • [-3, 6]

  • [3, 6]

  • [1, 2]

MCQ

उत्तर

[0, 6]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Vectors - Miscellaneous exercise 5 [पृष्ठ १८८]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
अध्याय 5 Vectors
Miscellaneous exercise 5 | Q I) 11) | पृष्ठ १८८

संबंधित प्रश्न

if `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`, , then express `vecb` in the form of `vecb = vec(b_1) + vec(b_2)`, where `vec(b_1)`  is parallel to `veca` and `vec(b_2)` is perpendicular to `veca`


If \[\overrightarrow{a}\], \[\overrightarrow{b}\], \[\overrightarrow{c}\] are the position vectors of the vertices of a triangle, then write the position vector of its centroid.


If \[\overrightarrow{a}\] and \[\overrightarrow{b}\] denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.


If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]


If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} - 3 \hat{k} \text{ and }\overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + 9 \hat{k} ,\]  find a unit vector parallel to \[\overrightarrow{a} + \overrightarrow{b}\].


If \[\overrightarrow{a} = x \hat{i} + 2 \hat{j} - z \hat{k}\text{ and }\overrightarrow{b} = 3 \hat{i} - y \hat{j} + \hat{k}\]  are two equal vectors, then write the value of x + y + z.


The position vectors of the points ABC are \[2 \hat{i} + \hat{j} - \hat{k} , 3 \hat{i} - 2 \hat{j} + \hat{k}\text{ and }\hat{i} + 4 \hat{j} - 3 \hat{k}\] respectively.
These points


If \[\vec{a}\text{ and }\vec{b}\] are two collinear vectors, then which of the following are incorrect?


If `veca` and `vecb` are non- collinear vectors, find the value of x such that the vectors `barα = (x - 2)veca + vecb` and `barβ = (3+2x)bara - 2barb` are collinear.


Find the value of λ for which the four points with position vectors `6hat"i" - 7hat"j", 16hat"i" - 19hat"j" - 4hat"k" , lambdahat"j" - 6hat"k"  "and"  2hat"i" - 5hat"j" + 10hat"k"` are coplanar.


If` vec"a" = 2hat"i" + 3hat"j" + + hat"k", vec"b" = hat"i" - 2hat"j" + hat"k"  "and"  vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`


The vector `bar"a"` is directed due north and `|bar"a"|` = 24. The vector `bar"b"` is directed due west and `|bar"b"| = 7`. Find `|bar"a" + bar"b"|`.


Find a vector in the direction of `bara = hati - 2hatj` that has magnitude 7 units.


Find the distance from (4, - 2, 6) to each of the following:
(a) The XY-plane
(b) The YZ-plane
(c) The XZ-plane
(d) The X-axis
(e) The Y-axis
(f) The Z-axis.


Find the coordinates of the point which is located three units behind the YZ-plane, four units to the right of XZ-plane, and five units above the XY-plane.


Find the coordinates of the point which is located in the YZ-plane, one unit to the right of the XZ- plane, and six units above the XY-plane.


Express the vector `bar"a" = 5hat"i" - 2hat"j" + 5hat"k"` as a sum of two vectors such that one is parallel to the vector `bar"b" = 3hat"i" + hat"k"` and other is perpendicular to `bar"b"`.


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")`


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"`


The XZ plane divides the line segment joining the points (3, 2, b) and (a, -4, 3) in the ratio ______.


If `overline"u"` and `overline"v"` are unit vectors and θ is the acute angle between them, then `2overline"u" xx 3overline"v"` is a unit vector for ______


For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______


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 area of the parallelogram whose adjacent sides are `hat"i" + hat"k"` and `2hat"i" + hat"j" + hat"k"` is ______.


If `|vec"a"|` = 3 and –1 ≤ k ≤ 2, then `|"k"vec"a"|` lies in the interval ______.


Classify the following measures as scalar and vector.

40°


Classify the following measures as scalar and vector.

40 watt


Let `bara, barb` and `barc` be three vectors, then `bara xx (barb xx barc) = (bara xx barb) xx barc` if


For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = - hati + hatj - hatk` find the unit vector in the direction of the vector `veca + vecb`.


Let the vectors `vec(a)` such `vec(b)` that `|veca|` = 3 and `|vecb| = sqrt(2)/3`, then `veca xx vecb` is a unit vector if the angle between `veca` and `vecb` is


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

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

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

(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`


If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be ______.


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

(i) `bar(PR)`  (ii) `bar(PM)`  (iii) `bar(QM)`


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.


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


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

(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×