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

State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar: abca¯.(b¯+c¯) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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")`

एका वाक्यात उत्तर

उत्तर

This is the scalar product of two vectors. Therefore, this expression is meaningful and it is a scalar.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Vectors - Miscellaneous exercise 5 [पृष्ठ १९२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 5 Vectors
Miscellaneous exercise 5 | Q II. 34) (j) | पृष्ठ १९२

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 D, E, F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC, write the value of \[\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF} .\]


Write a unit vector making equal acute angles with the coordinates axes.


If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin2 α + sin2 β + sin2 γ.


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 \[\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} \text{ and }\overrightarrow{b} = - \hat{i} + \hat{j} + \hat{k} .\]


If \[\overrightarrow{a} = \hat{i} + \hat{j} , \vec{b} = \hat{j} + \hat{k} \text{ and }\vec{c} = \hat{k} + \hat{i} ,\] write unit vectors parallel to \[\overrightarrow{a} + \overrightarrow{b} - 2 \overrightarrow{c} .\]


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.


Write a unit vector in the direction of \[\overrightarrow{PQ}\], where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.


If \[\left| \overrightarrow{a} \right| = 4\] and \[- 3 \leq \lambda \leq 2\], then write the range of \[\left| \lambda \vec{a} \right|\].


In a triangle OAC, if B is the mid-point of side AC and \[\overrightarrow{OA} = \overrightarrow{a} , \overrightarrow{OB} = \overrightarrow{b}\], then what is \[\overrightarrow{OC}\].


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 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 :

P(3, 2)


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.


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


Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).


Select the correct option from the given alternatives:

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


If `bar"OA" = bar"a" and bar"OB" = bar"b",` then show that the vector along the angle bisector of ∠AOB is given by `bar"d" = lambda(bar"a"/|bar"a"| + bar"b"/|bar"b"|).`


If P is orthocentre, Q is the circumcentre and G is the centroid of a triangle ABC, then prove that `bar"QP" = 3bar"QG"`.


Let bar"b" = 4hat"i" + 3hat"j" and bar"c" be two vectors perpendicular to each other in the XY-plane. Find the vector in the same plane having projection 1 and 2 along bar"b" and bar"c" respectively.


Show that no line in space can make angles `pi/6` and `pi/4` with X-axis and Y-axis.


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

`bar"a" xx (bar"b".bar"c")`


For any non-zero vectors a and b, [b a × b a] = ?


lf `overlinea` and `overlineb` be two unit vectors and θ is the angle between them, then `|overlinea - overlineb|` is equal to ______


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"`.


The vector with initial point P (2, –3, 5) and terminal point Q(3, –4, 7) is ______.


Find a unit vector in the direction of `vec"PQ"`, where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively


Classify the following as scalar and vector quantity.

Velocity


In Figure, identify the following vector.

Equal


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


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


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

lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is ______.


Evaluate the following.

`int x^3/(sqrt1 + x^4) `dx


In the triangle PQR, `bar(PQ)`= 2`bar a` and `bar(QR)`= 2`bar b` . 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)`

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×