Vector Triple...

Vector Triple Product

Trending Questions

Q. . If a, b, c are three unit vectors such that

a \times (b \times c) = \frac{1}{2}

b then the angles between a, b and a, c are

$90^{\circ}, 90^{\circ}$
$90^{\circ}, 60^{\circ}$
$60^{\circ}, 90^{\circ}$
$60^{\circ}, 30^{\circ}$

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Q. If

\to a, \to b, \to c

are non-coplanar unit vectors such that

\to a \times (\to b \times \to c) = \frac{(\to b + \to c)}{\sqrt{2}},

then the angle between

\to a

and

\to b

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

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Q. The unit vector which is orthogonal to the vector

3^i + 2^j + 6^k

and is coplanar with the vectors

2^i +^j +^k a n d^i -^j +^k

$\frac{2^i - 3^j}{\sqrt{13}}$
$\frac{4^i + 3^j - 3^k}{\sqrt{34}}$
$\frac{3^j -^k}{\sqrt{10}}$
$\frac{2^i - 6^j +^k}{\sqrt{41}}$

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Q. If

a^{x} = c^{q} = b

and

c^{y} = a^{z} = d

, then ___.

$\frac{x}{y} = \frac{q}{z}$
$x + y = q + z$
$x - y = q - z$
$x y = q z$

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Let $^a,^b a n d^c$ be three unit vectors such that
$^a \times (^b \times^c) = \frac{\sqrt{3}}{2} (^b +^c) .$ If
$^b$ is not parallel to $^c$ , then the angle between $^a$ and $^b$ is

$\frac{3 π}{4}$
$\frac{2 π}{3}$
$\frac{5 π}{6}$
$\frac{π}{2}$

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Q. Let ABC be a triangle and

\to a

\to b

and

\to c

be the position vectors of the point.

A, B

and

C,

respectively. External bisectors of

∠

a n d

\angle

C m e e t a t P w i t h t h e s i d e s o f t h e t r i a n g l e a s

\vec a, \vec b

a n d

\vec c

t h e p o s i t i o n v e c t o r s o f

P$ becomes

$\frac{(- b) b + (- c) c}{(b + c)}$
$(\frac{a + b + c}{3}) (a b c)$
$\frac{a a + (- b) b + (- c) c}{(a - b - c)}$
$\frac{a a + b b + c c}{(a + b + c)}$

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Q. If

\to a \times \to b = \to c

and

\to b \times \to c = \to a

, then

$\to a, \to b, \to c$ are orthogonal in pairs and $| \to a | = | \to b |$ and $| \to c | = 1$
$\to a, \to b, \to c$ are not orthogonal to each other
$\to a, \to b, \to c$ are orthogonal in pairs but $| \to a | \neq | \to c |$
$\to a, \to b, \to c$ are orthogonal but $| \to b | \neq 1$

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