हिंदी

State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar: abcd(a¯.b¯)×(c¯.d¯) - 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") xx (bar"c".bar"d")`

योग

उत्तर

This is meaningless because `bar"a".bar"b", bar"c".bar"d"` are scalars and cross product of two scalars is not defined.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Vectors - Miscellaneous exercise 5 [पृष्ठ १९२]

APPEARS IN

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

संबंधित प्रश्न

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


If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} , \vec{b} = \hat{j} + 2 \hat{k} ,\] write a unit vector along the vector \[3 \overrightarrow{a} - 2 \overrightarrow{b} .\]


Write the position vector of a point dividing the line segment joining points having position vectors \[\hat{i} + \hat{j} - 2 \hat{k} \text{ and }2 \hat{i} - \hat{j} + 3 \hat{k}\] externally in the ratio 2:3.


Find a unit vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k}\].


Find a unit vector in the direction of the vector \[\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + 6 \hat{k}\].


Write the position vector of the point which divides the join of points with position vectors \[3 \overrightarrow{a} - 2 \overrightarrow{b}\text{ and }2 \overrightarrow{a} + 3 \overrightarrow{b}\] in the ratio 2 : 1.


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


If three points A, B and C have position vectors \[\hat{i} + x \hat{j} + 3 \hat{k} , 3 \hat{i} + 4 \hat{j} + 7 \hat{k}\text{ and }y \hat{i} - 2 \hat{j} - 5 \hat{k}\] respectively are collinear, then (x, y) =


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


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

Q(–5, 1)


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

R(–11, –9)


In Figure, which of the following is not true?


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:

If l, m, n are direction cosines of a line then `"l"hat
"i" + "m"hat"j" + "n"hat"k"` is ______ 


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?


If two sides of a triangle are `hat"i" + 2hat"j" and hat"i" + hat"k"`, find the length of the third side.


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


a and b are non-collinear vectors. If p = (2x + 1) a - band q = (x - 2)a +b are collinear vectors, then x = ______.


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.


The 2 vectors `hat"j" + hat"k"` and `3hat"i" - hat"j" + 4hat"k"` represents the two sides AB and AC, respectively of a ∆ABC. The length of the median through A is ______.


Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.


If `vec"r" * vec"a" = 0, vec"r" * vec"b" = 0` and `vec"r" * vec"c" = 0` for some non-zero vector `vec"r"`, then the value of `vec"a" * (vec"b" xx vec"c")` is ______.


The values of k for which `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"` holds true are ______.


Classify the following measures as scalar and vector.

40°


Classify the following as scalar and vector quantity.

Distance


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")`

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.


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 + 2 hatj + 3hatk, - 3hati + 3hatj + 2hatk and 3hati + 4hatk` From a triangle or not.  


Evaluate the following.

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


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×