If | vec a | = 4,| vec b | = 2 and the angle between vec a and vec b is 6 then ( vec a vec b )^2 is equal to :

( vec a vec b )^2 = | vec a |^2| vec b |^2sin ^2 6 = 16 4 14 = 16

if a 4 b 2 and the angle between a and b is pi 6 then a

If $$\left| {\vec a} \right| = 4,\,\left| {\vec b} \right| = 2$$ and the angle between $${\vec a}$$ and $${\vec b}$$ is $$\frac{\pi }{6}$$ then $${\left( {\vec a \times \vec b} \right)^2}$$ is equal to :

A. $$48$$

B. $$16$$

C. $${\vec a}$$

D. none of these

Answer : $$16$$

Solution :
$${\left( {\vec a \times \vec b} \right)^2} = {\left| {\vec a} \right|^2}{\left| {\vec b} \right|^2}{\sin ^2}\frac{\pi }{6} = 16 \times 4 \times \frac{1}{4} = 16$$

Releted MCQ Question on
Geometry >> 3D Geometry and Vectors

Releted Question 1

The scalar $$\vec A.\left( {\vec B + \vec C} \right) \times \left( {\vec A + \vec B + \vec C} \right)$$ equals :

A. $$0$$

B. $$\left[ {\vec A\,\vec B\,\vec C} \right] + \left[ {\vec B\,\vec C\,\vec A} \right]$$

C. $$\left[ {\vec A\,\vec B\,\vec C} \right]$$

D. None of these

View Answer

Releted Question 2

For non-zero vectors $$\vec a,\,\vec b,\,\vec c,\,\left| {\left( {\vec a \times \vec b} \right).\vec c} \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\vec c} \right|$$ holds if and only if -

A. $$\vec a.\vec b = 0,\,\,\,\vec b.\vec c = 0$$

B. $$\vec b.\vec c = 0,\,\,\,\vec c.\vec a = 0$$

C. $$\vec c.\vec a = 0,\,\,\,\vec a.\vec b = 0$$

D. $$\vec a.\vec b = \vec b.\vec c = \vec c.\vec a = 0$$

View Answer

Releted Question 3

The volume of the parallelepiped whose sides are given by $$\overrightarrow {OA} = 2i - 2j,\,\,\overrightarrow {OB} = i + j - k,\,\,\overrightarrow {OC} = 3i - k,$$ is :

A. $$\frac{4}{{13}}$$

B. $$4$$

C. $$\frac{2}{7}$$

D. none of these

View Answer

Releted Question 4

The points with position vectors $$60i + 3j,\,\,40i - 8j,\,\,ai - 52j$$ are collinear if :

A. $$a = - 40$$

B. $$a = 40$$

C. $$a = 20$$

D. none of these

View Answer

If $$\left| {\vec a} \right| = 4,\,\left| {\vec b} \right| = 2$$ and the angle between $${\vec a}$$ and $${\vec b}$$ is $$\frac{\pi }{6}$$ then $${\left( {\vec a \times \vec b} \right)^2}$$ is equal to :

Releted MCQ Question on
Geometry >> 3D Geometry and Vectors

The scalar $$\vec A.\left( {\vec B + \vec C} \right) \times \left( {\vec A + \vec B + \vec C} \right)$$ equals :

For non-zero vectors $$\vec a,\,\vec b,\,\vec c,\,\left| {\left( {\vec a \times \vec b} \right).\vec c} \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\vec c} \right|$$ holds if and only if -

The volume of the parallelepiped whose sides are given by $$\overrightarrow {OA} = 2i - 2j,\,\,\overrightarrow {OB} = i + j - k,\,\,\overrightarrow {OC} = 3i - k,$$ is :

The points with position vectors $$60i + 3j,\,\,40i - 8j,\,\,ai - 52j$$ are collinear if :

Practice More Releted MCQ Question on
3D Geometry and Vectors

Practice More MCQ Question on Maths Section

If $$\left| {\vec a} \right| = 4,\,\left| {\vec b} \right| = 2$$ and the angle between $${\vec a}$$ and $${\vec b}$$ is $$\frac{\pi }{6}$$ then $${\left( {\vec a \times \vec b} \right)^2}$$ is equal to :

Releted MCQ Question on Geometry >> 3D Geometry and Vectors

The scalar $$\vec A.\left( {\vec B + \vec C} \right) \times \left( {\vec A + \vec B + \vec C} \right)$$ equals :

For non-zero vectors $$\vec a,\,\vec b,\,\vec c,\,\left| {\left( {\vec a \times \vec b} \right).\vec c} \right| = \left| {\vec a} \right|\left| {\vec b} \right|\left| {\vec c} \right|$$ holds if and only if -

The volume of the parallelepiped whose sides are given by $$\overrightarrow {OA} = 2i - 2j,\,\,\overrightarrow {OB} = i + j - k,\,\,\overrightarrow {OC} = 3i - k,$$ is :

The points with position vectors $$60i + 3j,\,\,40i - 8j,\,\,ai - 52j$$ are collinear if :

Practice More Releted MCQ Question on 3D Geometry and Vectors

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Geometry >> 3D Geometry and Vectors

Practice More Releted MCQ Question on
3D Geometry and Vectors