If $\stackrel{\to }{\mathrm{a}}$ is a vector and x is a non-zero scalar, then

(A) xa is a vector in the direction of $\stackrel{\to }{\mathrm{a}}$

(B)  xa is a vector collinear to $\stackrel{\to }{\mathrm{a}}$

(C)  xa and $\stackrel{\to }{\mathrm{a}}$ have independent directions

(D)  xa is a vector perpendicular to $\stackrel{\to }{\mathrm{a}}$

Concept Questions :-

Scalar Product
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Difficulty Level:

A vector that is perpendicular to both the vectors $\stackrel{\to }{\mathrm{a}}=\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$ and $\stackrel{\to }{\mathrm{b}}=\stackrel{^}{\mathrm{i}}-\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$ is

(A)  $-\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{k}}$

(B)  $-\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$

(C)  $\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$

(D)  $\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{k}}$

Concept Questions :-

Scalar Product
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Difficulty Level:

If $\mathrm{\theta }$ is the angle between vectors $\stackrel{\to }{\mathrm{a}}$ and $\stackrel{\to }{\mathrm{b}}$, and $|\stackrel{\to }{\mathrm{a}}×\stackrel{\to }{\mathrm{b}}|=\stackrel{\to }{\mathrm{a}}.\stackrel{\to }{\mathrm{b}}$, then $\mathrm{\theta }$ is equal to

(A)  $0°$

(B)  $180°$

(C)  $135°$

(D)  $45°$

Concept Questions :-

Vector Product
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Difficulty Level:

The vector $\stackrel{\to }{\mathrm{b}}$, which is collinear with the vector $\stackrel{\to }{\mathrm{a}}$=(2, 1, -1) and satisfies the condition $\stackrel{\to }{\mathrm{a}}$.$\stackrel{\to }{\mathrm{b}}$=3, is

(A)  (1, 1/2, -1/2)

(B)  (2/3, 1/3, -1/3)

(C)  (1/2, 1/4, -1/4)

(D)  (1, 1, 0)

Concept Questions :-

Scalar Product
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Difficulty Level:

If $3\stackrel{^}{\mathrm{i}}+2\stackrel{^}{\mathrm{j}}+8\stackrel{^}{\mathrm{k}}$ and $2\stackrel{^}{\mathrm{i}}+\mathrm{x}\stackrel{^}{\mathrm{j}}+\stackrel{^}{\mathrm{k}}$ are at right angle then x=

(A)  7

(B)  -7

(C)  5

(D)  -4

Concept Questions :-

Scalar Product
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Difficulty Level:

If a, b, c are three non-zero vectors such that $\stackrel{\to }{\mathrm{a}}+\stackrel{\to }{\mathrm{b}}+\stackrel{\to }{\mathrm{c}}=0$ the value of $\stackrel{\to }{\mathrm{a}}.\stackrel{\to }{\mathrm{b}}+\stackrel{\to }{\mathrm{b}}.\stackrel{\to }{\mathrm{c}}+\stackrel{\to }{\mathrm{c}}.\stackrel{\to }{\mathrm{a}}$ is

(A)  Less than zero

(B)  equal to zero

(C)  greater than zero

(D)  3

Concept Questions :-

Scalar Product
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Difficulty Level:

Let  be distinct real numbers. The points with position vectors

(A)  are collinear

(B)  from an equilateral triangle

(C) form an isosceles triangle

(D)  from a right angled triangle

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

Two vectors $\stackrel{\to }{\mathrm{a}}$ and $\stackrel{\to }{\mathrm{b}}$ inclined at an angle $\mathrm{\theta }$ w.r.t. each other have a resultant $\stackrel{\to }{\mathrm{c}}$ which makes an angle $\mathrm{\beta }$ with $\stackrel{\to }{\mathrm{a}}$. If the directions of $\stackrel{\to }{\mathrm{a}}$ and $\stackrel{\to }{\mathrm{b}}$ are interchanged, then the resultant will have the same

(A)  magnitude

(B)  direction

(C)  magnitude as well as direction

(D)  neither magnitude nor direction

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Difficulty Level:

Two vectors $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ lie in a plane. Another vector $\stackrel{\to }{\mathrm{C}}$ lies outside this plane. The resultant $\stackrel{\to }{\mathrm{A}}+\stackrel{\to }{\mathrm{B}}+\stackrel{\to }{\mathrm{C}}$ of these three vectors

(A)  can be zero

(B)  cannot be zero

(C)  lies in the plane of

(D)  lies in the plane of

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

The vector sum of the forces of 10 N and 6 N can be

(A)  2 N

(B)  8 N

(C)  18 N

(D)  20 N

Concept Questions :-

Resultant of Vectors
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Difficulty Level: