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

प्रश्न

Select the correct option from the given alternatives:

If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar unit vectors such that $\bar{a} \times (\bar{b} \times \bar{c}) = \frac{\bar{b} + \bar{c}}{\sqrt{2}}$ , then the angle between $\bar{a} and \bar{b}$ is

विकल्प

$\frac{3 π}{4}$
$\frac{π}{4}$
$\frac{π}{2}$
$π$

MCQ

उत्तर

$\frac{3 π}{4}$

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Vectors and Their Types

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q I) 20)Q I) 19)Q II. 1)

अध्याय 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

अध्याय 5 Vectors
Miscellaneous exercise 5 | Q I) 20) | पृष्ठ १८९

संबंधित प्रश्न

If $\vec{a}$ , $\vec{b}$ , $\vec{c}$ represent the sides of a triangle taken in order, then write the value of $\vec{a} + \vec{b} + \vec{c} .$

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 $\vec{A B} + \vec{B C} + \vec{C A} .$

If G denotes the centroid of ∆ABC, then write the value of $\vec{G A} + \vec{G B} + \vec{G C} .$

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.

If $| \vec{a} | = 4$ and $- 3 \leq λ \leq 2$ , then write the range of $| λ \vec{a} |$ .

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

In a regular hexagon ABCDEF, A $\vec{B}$ = a, B $\vec{C}$ = $\vec{b} and \vec{C D} = \vec{c}$ .
Then, $\vec{A E}$ =

If $\vec{a}$ , $\vec{b}$ , $\vec{c}$ and $\vec{d}$ are the position vectors of points A, B, C, D such that no three of them are collinear and $\vec{a} + \vec{c} = \vec{b} + \vec{d},$ then ABCD is a

The position vectors of the points A, B, C are $2 \hat{i} + \hat{j} - \hat{k}, 3 \hat{i} - 2 \hat{j} + \hat{k} and \hat{i} + 4 \hat{j} - 3 \hat{k}$ respectively.
These points

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

Q(–5, 1)

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.

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k}$ and $3 \hat{i} + 4 \hat{k}$ form a triangle or not.

In the given figure express $\bar{c}$ and $\bar{d}$ in terms of $\bar{a}$ and $\bar{b}$ .

Find a vector in the direction of $\bar{a} = \hat{i} - 2 \hat{j}$ that has magnitude 7 units.

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

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 ABC is a triangle whose orthocentre is P and the circumcentre is Q, prove that $\bar{PA} + \bar{PB} + \bar{PC} = 2 \bar{PQ} .$

Find two unit vectors each of which makes equal angles with bar"u", bar"v" and bar"w" where bar"u" = 2hat"i" + hat"j" - 2hat"k", bar"v" = hat"i" + 2hat"j" - 2hat"k", bar"w" = 2hat"i" - 2hat"j" + hat"k".

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.

Find the angle between the lines whose direction cosines are given by the equations 6mn - 2nl + 5lm = 0, 3l + m + 5n = 0.

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

$\bar{a} \times (\bar{b} \times \bar{c})$

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

$\bar{a} . (\bar{b} . \bar{c})$

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

$(\bar{a} . \bar{b}) \bar{c}$

lf $\bar{a}$ and $\bar{b}$ be two unit vectors and θ is the angle between them, then $| \bar{a} - \bar{b} |$ is equal to ______

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

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{π}{4}$ and $\frac{π}{2}$ with y and z-axes, respectively.

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

The vector $\vec{a} + \vec{b}$ bisects the angle between the non-collinear vectors $\vec{a}$ and $\vec{b}$ if ______.

If $\vec{r} \cdot \vec{a} = 0, \vec{r} \cdot \vec{b} = 0$ and $\vec{r} \cdot \vec{c} = 0$ for some non-zero vector $\vec{r}$ , then the value of $\vec{a} \cdot (\vec{b} \times \vec{c})$ is ______.

If two or more vectors are parallel to the same line, such vectors are known as:

For given vectors, $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{b} = - \hat{i} + \hat{j} - \hat{k}$ find the unit vector in the direction of the vector $\vec{a} + \vec{b}$ .

Let the vectors $\vec{a}$ such $\vec{b}$ that $| \vec{a} |$ = 3 and $| \vec{b} | = \frac{\sqrt{2}}{3}$ , then $\vec{a} \times \vec{b}$ is a unit vector if the angle between $\vec{a}$ and $\vec{b}$ is

If $\vec{a} = \hat{i} - \hat{j} + 7 \hat{k}$ and $\vec{b} = 5 \hat{i} - \hat{j} + λ \hat{k}$ , then find the value of λ so that the vectors $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$ are orthogonal.

Evaluate the following.

$\int \frac{x^{3}}{\sqrt{1} + x^{4}}$ dx

In the triangle PQR, $\bar{P Q} = 2 \bar{a}$ and $\bar{Q R} = 2 \bar{b}$ . The mid-point of PR is M. Find following vectors in terms of $\bar{a} and \bar{b}$ .

(i) $\bar{P R}$ (ii) $\bar{P M}$ (iii) $\bar{Q M}$

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) $\bar{QM}$

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k}$ and $3 \hat{i} + 4 \hat{k}$ form a triangle or not.

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k} and 3 \hat{i} + 4 \hat{k}$ form a triangle or not.

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

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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

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