English

Select the correct option from the given alternatives: If abca¯,b¯,c¯ are non-coplanar unit vectors such that abcbca¯×(b¯×c¯)=b¯+c¯2, then the angle between aandba¯ and b¯ is - Mathematics and Statistics

Advertisements
Advertisements

Question

Select the correct option from the given alternatives:

If `bar"a", bar"b", bar"c"` are non-coplanar unit vectors such that `bar"a"xx (bar"b"xxbar"c") = (bar"b"+bar"c")/sqrt2`, then the angle between `bar"a"  "and"  bar"b"` is 

Options

  • `(3pi)/4`

  • `pi/4`

  • `pi/2`

  • `pi`

MCQ

Solution

`(3pi)/4`

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Vectors - Miscellaneous exercise 5 [Page 189]

APPEARS IN

RELATED QUESTIONS

If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of \[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} .\]


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


If points A (60 \[\hat{i}\] + 3 \[\hat{j}\]), B (40 \[\hat{i}\] − 8 \[\hat{j}\]) and C (a \[\hat{i}\] − 52 \[\hat{j}\]) are collinear, then a is equal to


If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then \[O \vec{A} + O \vec{B} + O \vec{C} + O \vec{D} =\] 


If ABCDEF is a regular hexagon, then \[\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}\] equals

 


ABCD is a parallelogram with AC and BD as diagonals.
Then, \[\overrightarrow{AC} - \overrightarrow{BD} =\] 


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

Q(–5, 1)


In Figure, which of the following is not true?


If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.


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


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?


Let `bara = hati - hatj, barb = hatj - hatk, barc = hatk - hati.` If `bard` is a unit vector such that `bara * bard = 0 = [(barb, barc, bard)]`, then `bard` equals ______.


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 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"`.


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"|(bar"b".bar"c")`


If `bar"a", bar"b", bar"c"` are three non-coplanar vectors show that `(bar"a".(bar"b" xx bar"c"))/((bar"c" xx bar"a").bar"b") + (bar"b".(bar"a" xx bar"c"))/((bar"c" xx bar"a").bar"b") = 0`


The points A(- a, -b), B (0, 0), C(a, b) and D(a2 , ab) are ______.


If A, B, C and D are (3, 7, 4), (5, -2, - 3), (- 4, 5, 6) and(1, 2, 3) respectively, then the volume of the parallelopiped with AB, AC and AD as the co-terminus edges, is ______ cubic units.


Find a vector of magnitude 11 in the direction opposite to that of `vec"PQ"` where P and Q are the points (1, 3, 2) and (–1, 0, 8), respectively.


The angle between the vectors `hat"i" - hat"j"` and `hat"j" - hat"k"` is ______.


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


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"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


Classify the following as scalar and vector quantity.

Velocity


Four vectors `veca, vecb, vecc` and `vecx` satisfy the relation `(veca.vecx)vecb = vecc + vecx` where `vecb * veca` ≠ 1. The value of `vecx` in terms of `veca, vecb` and `vecc` is equal to


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 `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.


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


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)`

Consider the following statements and choose the correct option:

Statement 1: If `veca` and `vecb` represents two adjacent sides of a parallelogram then the diagonals are represented by `veca + vecb` and `veca - vecb`.

Statement 2: If `veca` and `vecb` represents two diagonals of a parallelogram then the adjacent sides are represented by `2(veca + vecb)` and `2(veca - vecb)`.

Which of the following is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×