मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

पर्याय

  • [0, 6]

  • [-3, 6]

  • [3, 6]

  • [1, 2]

MCQ

उत्तर

[0, 6]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Vectors - Miscellaneous exercise 5 [पृष्ठ १८८]

APPEARS IN

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

संबंधित प्रश्‍न

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 \[\overrightarrow{a}\] is a non-zero vector of modulus a and m is a non-zero scalar such that m \[\overrightarrow{a}\] is a unit vector, write the value of m.


Write the position vector of a point dividing the line segment joining points A and B with position vectors \[\vec{a}\] and \[\vec{b}\] externally in the ratio 1 : 4, where \[\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} \text{ and }\overrightarrow{b} = - \hat{i} + \hat{j} + \hat{k} .\]


\[\text{ If } \overrightarrow{a} = 3 \hat{i} - \hat{j} - 4 \hat{k} , \overrightarrow{b} = - 2 \hat{i} + 4 \hat{j} - 3 \hat{k} \text{ and }\overrightarrow{c} = \hat{i} + 2 \hat{j} - \hat{k} ,\text{ find }\left| 3 \overrightarrow{a} - 2 \overrightarrow{b} + 4 \overrightarrow{c} \right| .\]

Write a unit vector in the direction of the sum of the vectors \[\overrightarrow{a} = 2 \hat{i} + 2 \hat{j} - 5 \hat{k}\] and \[\overrightarrow{b} = 2 \hat{i} + \hat{j} - 7 \hat{k}\].


Find the value of 'p' for which the vectors \[3 \hat{i} + 2 \hat{j} + 9 \hat{k}\] and \[\hat{i} - 2p \hat{j} + 3 \hat{k}\] are parallel.


If \[\vec{a} , \vec{b}\] are the vectors forming consecutive sides of a regular hexagon ABCDEF, then the vector representing side CD is 


If \[\vec{a} , \vec{b} , \vec{c}\] are three non-zero vectors, no two of which are collinear and the vector \[\vec{a} + \vec{b}\] is collinear with \[\vec{c} , \vec{b} + \vec{c}\] is collinear with \[\vec{a} ,\] then \[\vec{a} + \vec{b} + \vec{c} =\]

 


If OACB is a parallelogram with \[\overrightarrow{OC} = \vec{a}\text{ and }\overrightarrow{AB} = \vec{b} ,\] then \[\overrightarrow{OA} =\]


Find the position vector of the mid-point of the vector joining the points

\[P \left( 2 \hat{i} - 3\hat{ j} + 4 \hat{k} \right)\text{ and } Q \left( 4 \hat{i} + \hat{j} - 2 \hat{k} \right) .\]

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


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.


Select the correct option from the given alternatives:

Let α, β, γ be distinct real numbers. The points with position vectors `alphahat"i" + betahat"j" + gammahat"k",  betahat"i" + gammahat"j" + alphahat"k",   gammahat"i" + alphahat"j" + betahat"k"`


Find the component form of `bar"a"` if it lies in YZ-plane makes 60° with positive Y-axis and `|bar"a"| = 4`.


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


If `bar"a", bar"b", bar"c"` are unit vectors such that `bar"a" + bar"b" + bar"c" = bar0,` then find the value of `bar"a".bar"b" + bar"b".bar"c" + bar"c".bar"a".`


Express `hat"i" + 4hat"j" - 4hat"k"` as the linear combination of the vectors `2hat"i" - hat"j" + 3hat"k", hat"i" - 2hat"j" + 4hat"k"` and `- hat"i" + 3hat"j" - 5hat"k"`.


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"`


For any vectors `bar"a", bar"b", bar"c"` show that `(bar"a" + bar"b" + bar"c") xx bar"c" + (bar"a" + bar"b" + bar"c") xx bar"b" + (bar"b" - bar"c") xx bar"a" = 2bar"a" xx bar"c"`


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 ______


If the vectors `xhat"i" - 3hat"j" + 7hat"k" and hat"i" + "y"hat"j" - "z"hat"k"` are collinear then the value of `"xy"^2/"z"` is equal.


Find the unit vector in the direction of the sum of the vectors `vec"a" = 2hat"i" - hat"j" + 2hat"k"` and `vec"b" = -hat"i" + hat"j" + 3hat"k"`.


Find a vector `vec"r"` of magnitude `3sqrt(2)` units which makes an angle of `pi/4` and `pi/2` with y and z-axes, respectively.


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 ______.


Classify the following measures as scalar and vector.

10-19 coulomb


Classify the following as scalar and vector quantity.

Work done


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


If points P(4, 5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is ______.


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


Check whether the vectors `2 hati + 2 hatj + 3 hatk, -3 hati + 3 hatj + 2 hatk  "and"  3 hati + 4 hatk`  from 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 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.


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

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

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×