Multiplication Of Vectors MCQ - Practice Questions & Answers

Solve by difficulty

If $\vec{a},\; \vec{b}$ are unit vectors such that $(\vec{a}+\vec{b}).[( 2\vec{a}+3\vec{b} )\times ( 3\vec{a}-2\vec{b})\;]=0,$ then angle between $\vec{a} \; and\; \; \vec{b}$ is -

$0$

$\frac{\pi }{2}$

$\pi$

Indeterminate

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Vectors $\underset{A}{\rightarrow},\underset{B}{\rightarrow}\:and\:\underset{C}{\rightarrow}$ are such that $\underset{A}{\rightarrow}.\underset{B}{\rightarrow}=0\:and\:\underset{A}{\rightarrow}.\underset{C}{\rightarrow}=0$ . Then the vector parallel to $\underset{A}{\rightarrow}$ is

$\underset{B}{\rightarrow}\:and\:\underset{C}{\rightarrow}$

$\underset{A}{\rightarrow}\times \underset{B}{\rightarrow}$

$\underset{B}{\rightarrow}+ \underset{C}{\rightarrow}$

$\underset{B}{\rightarrow}\times \underset{C}{\rightarrow}$

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Concepts Covered - 1

MULTIPLICATION OF VECTORS

If a vector is multiplied by any scalar

$\vec{Z}= n\cdot \vec{Y}$

(n=1,2,3..)

Vector $\times$ Scalar $=$ Vector

We get again a vector.

2. If a vector is multiplied by any real number (eg 2 or -2) then again, we get a vector quantity.

E.g.

If $\vec{A}$ is multiplied by 2 then direction of the resultant vector is the same as that of the given vector.

$Vector =2\vec{A}$

If $\vec{A}$ is multiplied by (-2), then the direction of resultant is opposite to that of given vector.

$Vector =-2\vec{A}$

Scalar or Dot or Inner Product

Scalar product of two vector $\vec{A}$ & $\vec{B}$ written as $\vec{A}$ $\cdot$ $\vec{B}$
$\vec{A}$ $\cdot$ $\vec{B}$ is a scalar quantity given by the product of magnitude of $\vec{A}$ & $\vec{B}$ and the cosine of smaller angle between them.

$\vec{A}\cdot \vec{B}= A\, B\cdot \cos \Theta$

Figure showing representation of scalar products of vectors.

Vector or cross product

Vector or cross product of two vector $\vec{A}$ & $\vec{B}$ written as $A\times B$
$A\times B$ is a single vector whose magnitude is equal to product of magnitude of $\vec{A}$ & $\vec{B}$ and the sine of smaller angle $\Theta$ between them.
$\vec A\times \vec B= A\, B\sin \Theta$