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Select the correct option from the given alternatives: The value of ijkjikkiji^.(j^×k^)+j^.(i^×k^)+k^.(i^×j^) is - Mathematics and Statistics

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प्रश्न

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

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Vectors - Miscellaneous exercise 5 [पृष्ठ १८९]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 12 Standard HSC Maharashtra State Board
पाठ 5 Vectors
Miscellaneous exercise 5 | Q I) 17) | पृष्ठ १८९

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 \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]


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


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 \[\overrightarrow{a} = \hat{i} + 2 \hat{j} - 3 \hat{k} \text{ and }\overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + 9 \hat{k} ,\]  find a unit vector parallel to \[\overrightarrow{a} + \overrightarrow{b}\].


If \[\overrightarrow{a} = x \hat{i} + 2 \hat{j} - z \hat{k}\text{ and }\overrightarrow{b} = 3 \hat{i} - y \hat{j} + \hat{k}\]  are two equal vectors, then write the value of x + y + z.


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 \[\left| \lambda \vec{a} \right|\].


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


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

P(3, 2)


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

R(–11, –9)


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

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

Find the value of λ for which the four points with position vectors `6hat"i" - 7hat"j", 16hat"i" - 19hat"j" - 4hat"k" , lambdahat"j" - 6hat"k"  "and"  2hat"i" - 5hat"j" + 10hat"k"` are coplanar.


Find the coordinates of the point which is located three units behind the YZ-plane, four units to the right of XZ-plane, and five units above the XY-plane.


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:

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 


Find the lengths of the sides of the triangle and also determine the type of a triangle:

A(2, -1, 0), B(4, 1, 1), C(4, -5, 4)


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


ABCD is a parallelogram. E, F are the midpoints of BC and CD respectively. AE, AF meet the diagonal BD at Q and P respectively. Show that P and Q trisect DB.


If a parallelogram is constructed on the vectors `bar"a" = 3bar"p" - bar"q", bar"b" = bar"p" + 3bar"q" and |bar"p"| = |bar"q"| = 2` and angle between `bar"p" and bar"q"` is `pi/3,` and angle between lengths of the sides is `sqrt7 : sqrt13`.


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 non zero vector, a, b, c a · ((b + c) × (a + b + c)] = ______.


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.


The unit vector perpendicular to the vectors `hat"i" - hat"j"` and `hat"i" + hat"j"` forming a right handed system 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


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"` are unit vectors such that `vec"a" + vec"b" + vec"c"` = 0, then the value of `vec"a" * vec"b" + vec"b" * vec"c" + vec"c" * vec"a"` is ______.


The formula `(vec"a" + vec"b")^2 = vec"a"^2 + vec"b"^2 + 2vec"a" xx vec"b"` is valid for non-zero vectors `vec"a"` and `vec"b"`


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


Which of the following measures as vector?


If `veca = hati - hatj + 7hatk` and `vecb = 5hati - hatj + λhatk`, then find the value of λ so that the vectors `veca + vecb` and `veca - vecb` are orthogonal.


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)=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) = 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)`

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


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