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Vector Algebra

Multiple Choice Questions

371.
Let a, b and c be distinct non-negative numbers. If the vectors $straight a straight i with hat on top space plus straight a space straight j with hat on top space plus space straight c straight k with hat on top comma space space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space$

the Geometric Mean of a and b

the Arithmetic Mean of a and b

equal to zero

equal to zero

the Geometric Mean of a and b

Vector space straight a space straight i with hat on top space plus straight a straight j with hat on top space plus straight c straight k with hat on top space comma space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space are space coplanar open vertical bar table row straight a straight a straight c row 1 0 1 row straight c straight c straight b end table close vertical bar space equals space 0 rightwards double arrow space straight c squared space equals ab therefore space straight a comma straight b comma straight c space are space in space straight G. straight P

117 Views

372.

If $straight a with rightwards arrow on top comma straight b with rightwards arrow on top comma space straight c with rightwards arrow on top$ are non -coplanar vector λ is a real number then

$open square brackets straight lambda left parenthesis straight a with rightwards arrow on top space plus straight b with rightwards arrow on top right parenthesis space straight lambda squared space straight b with rightwards arrow on top straight lambda space straight c with rightwards arrow on top close square brackets space equals space open square brackets straight a with rightwards arrow on top space straight b with rightwards arrow on top space plus straight c with rightwards arrow on top straight b with rightwards arrow on top close square brackets space for$

exactly one value of λ
no value of λ
exactly three values of λ
exactly three values of λ

261 Views

373.

Let space straight a with rightwards arrow on top space equals space straight i with hat on top space minus straight k with hat on top comma space straight b with rightwards arrow on top space equals space straight x straight i with hat on top space plus straight j with hat on top space plus left parenthesis 1 minus straight x right parenthesis space straight k with hat on top space and space straight c with rightwards arrow on top space equals space straight y straight i with hat on top space plus straight x space straight j with hat on top space plus left parenthesis 1 plus straight x minus straight y right parenthesis straight k with hat on top space. Then space left square bracket straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top right square bracket

depends on

only y
only x
both x and y
both x and y

99 Views

374.

The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is

2 : 1
$3 colon square root of 2$
3:2
3:2

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375.

Let $straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on top$ be three non-zero vectors such that no two of these are collinear. If the vector $straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top$ is collinear with $straight c with rightwards arrow on top space and space straight b with rightwards arrow on top space plus 3 straight c with rightwards arrow on top$ is collinear with $straight a with rightwards arrow on top$ (λ being some non-zero scalar) then $straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top space plus 6 straight c with rightwards arrow on top$ equals

λ $straight a with rightwards arrow on top$
λ $straight b with rightwards arrow on top$
λ $straight c with rightwards arrow on top$
λ $straight c with rightwards arrow on top$

147 Views

376.

A particle is acted upon by constant forces $4 space straight i with hat on top space plus straight j with hat on top space minus 3 straight k with hat on top space space and 3 space straight i with hat on top space plus straight j with hat on top space minus straight k with hat on top$ which displace it from a point $straight i with hat on top space plus 2 straight j with hat on top space plus 3 straight k with hat on top space to space the space point space 5 straight i with hat on top space plus space 4 straight j with hat on top space plus straight k with hat on top. space$ The work done in standard units by the forces is given by

116 Views

377.

If space straight a with bar on top comma space straight b with bar on top comma straight c with bar on top space

are non-coplanar vectors and λ is a real number, then the vectors

straight a with bar on top space plus 2 straight b with bar on top space plus 3 straight c with bar on top space comma space straight lambda straight b with bar on top space plus 4 space straight c with bar on top space and space left parenthesis 2 straight lambda space minus 1 right parenthesis straight c with bar on top

are non-coplanar for

all values of λ
all except one value of λ
all except two values of λ
all except two values of λ

141 Views

378.

Let $straight u with bar on top comma space straight v with bar on top space comma space straight w with bar on top$ be such that $vertical line top enclose straight u vertical line space equals space vertical line top enclose straight v vertical line space equals space 2 comma space vertical line top enclose straight w vertical line space equals space 3$ If the projection $top enclose straight v space along space top enclose straight u$ is equal to that of $space top enclose straight w space along space top enclose top enclose straight u end enclose space and space top enclose straight v comma space top enclose straight w space$ are perpendicular to each other then $vertical line top enclose straight u space minus top enclose straight v space plus top enclose straight w vertical line$ equals

2
$square root of 14$
$square root of 12$
$square root of 12$

118 Views

379.

Let $top enclose straight a space comma top enclose straight b space and space top enclose straight c space$ be non-zero vectors such that $left parenthesis top enclose straight a space straight x space top enclose straight b right parenthesis space straight x space top enclose straight c space equals space 1 third space vertical line straight b with bar on top vertical line vertical line straight c with bar on top vertical line vertical line straight a with bar on top vertical line$ If θ is the acute angle between the vectors $top enclose straight b space and space top enclose straight c comma$ then sin θ equals

1/3
$fraction numerator square root of 1 over denominator 3 end fraction$
2/3
2/3

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380.

Let $\vec{u}$ be a vector coplanar with the vectors a $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} a n d \vec{b} = \hat{j} + \hat{k} .$ $i f \vec{u} i s p e r p e n d i c u l a r t o \vec{a} a n d \vec{u} . \vec{b} = 24, t h e n | \vec{u} | i s e q u a l t o :$

Previous Year Papers

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Multiple Choice Questions

371. Let a, b and c be distinct non-negative numbers. If the vectors the Geometric Mean of a and b the Arithmetic Mean of a and b equal to zero equal to zero