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: abc(a¯.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 a scalar multiplication of a vector. Therefore, this expression is meaningful and it is a vector.

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) (h) | पृष्ठ १९२

संबंधित प्रश्‍न

If G denotes the centroid of ∆ABC, then write the value of \[\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC} .\]


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


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

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 \[\overrightarrow{a} + \overrightarrow{b}\].


For what value of 'a' the vectors \[2 \hat{i} - 3 \hat{j} + 4 \hat{k} \text{ and }a \hat{i} + 6 \hat{j} - 8 \hat{k}\]  are collinear?


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.


In a regular hexagon ABCDEF, A \[\vec{B}\] = a, B \[\vec{C}\] = \[\overrightarrow{b}\text{ and }\overrightarrow{CD} = \vec{c}\].
Then, \[\overrightarrow{AE}\] =


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

S(4, –3)


Show that the four points having position vectors

\[6 \hat { i} - 7 \hat { j} , 16 \hat {i} - 19 \hat {j}- 4 \hat {k} , 3 \hat {j} - 6 \hat {k} , 2 \hat {i} + 5 \hat {j} + 10 \hat {k}\] are not coplanar.


OABCDE is a regular hexagon. The points A and B have position vectors `bar"a"` and `bar"b"` respectively referred to the origin O. Find, in terms of `bar"a"` and `bar"b"` the position vectors of C, D and E.


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"`


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


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


Two sides of a parallelogram are `3hat"i" + 4hat"j" - 5hat"k"` and  `-2hat"j" + 7hat"k"`. Find the unit vectors parallel to the diagonals.


Dot product of a vector with vectors `3hat"i" - 5hat"k",  2hat"i" + 7hat"j" and hat"i" + hat"j" + hat"k"` are respectively -1, 6 and 5. Find the vector.


Find the acute angle between the curves at their points of intersection, y = x2, y = x3.


The vector eqliation of line 2x - 2 = 3y + 1 = 6z - 2 is


If the vectors `overlinea = 2hati - qhatj + 3hatk` and `overlineb = 4hati - 5hatj + 6hatk` are collinear, then the value of q is ______


For 0 < θ < π, if A = `[(costheta, -sintheta), (sintheta, costheta)]`, then ______ 


lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______ 


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


If `vec"a" = hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `6vec"b"`


If `vec"a", vec"b", vec"c"` determine the vertices of a triangle, show that `1/2[vec"b" xx vec"c" + vec"c" xx vec"a" + vec"a" xx vec"b"]` gives the vector area of the triangle. Hence deduce the condition that the three points `vec"a", vec"b", vec"c"` are collinear. Also find the unit vector normal to the plane of the triangle.


Classify the following as scalar and vector quantity.

Force


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


Find `|vecx|`, if for a unit vector `veca, (vecx - veca) * (vecx + veca)` = 12


In the triangle PQR, `bar("P""Q")`= `2 bar"a"` and `bar ("QR")` = `2 barb`.The mid - point of PR is M. Find following vector in term of  `bar a ` and `barb.`

  1. `bar("P""R")` 
  2. `bar("P""M")`
  3. `bar("Q""M")`

Find the value of λ for which the points (6, – 1, 2), (8, – 7, λ) and (5, 2, 4) are collinear.


Check whether the vectors `2hati +2hatj+3hatk, -3hati +3hatj +2hatk 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")`.


If `hata` is unit vector and `(2vecx - 3hata)*(2vecx + 3hata)` = 91, find the value of `|vecx|`.


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


In the triangle PQR, `bar"PQ" = bar"2a", bar"QR" = bar"2b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:

(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. 


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×