Vector Triple...

Vector Triple Product

Trending Questions

Q. If

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

and

\to y \cdot \to z = 1

. Vector

\to z

$\frac{γ}{| \to a \times \to b |^{2}} [\to a + \to b \times (\to a \times \to b)]$
$\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b - \to a \times (\to a \times \to b)]$
$\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b + \to b \times (\to a \times \to b)]$
None of these

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Q. If

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

and

\to y \cdot \to z = 1

. Vector

\to y

$\frac{\to a \times \to b}{γ}$
$\to a + \frac{\to a \times \to b}{γ}$
$\to a + \to b + \frac{\to a \times \to b}{γ}$
None of these.

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Q. Statement

1

: If

\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k

and

\to C =^i + 2^j +^k

, then

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243

Statement

2

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |

Both the statements are true and statement $2$ is the correct explanation for Statement $1$
Both the statements are true but Statement $2$ is not the correct explanation for Statement $1$
Statement $1$ is false and Statement $2$ is true
Statement $1$ is false and Statement $2$ is false

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Q. If

\to x, \to y, \to z

are units vectors such that

\to x + \to y + \to z = \to a

(\to x \times \to y) \times \to z = \to b

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2,

then which of the following is FALSE?

$\to y$ is perpendicular to $\to z$
$\to y$ is perpendicular to $\to b$
Angle between $\to x$ and $\to y$ is acute.
Angle between $\to x$ and $\to z$ is obtuse.

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Let $Δ P Q R$ be a triangle. Let a = QR, b = RP and c = PQ. If $| a | = 12, | b | = 4 \sqrt{3}$ and $b . c = 24,$ then which of the following is/are true ?

$\frac{| c |^{2}}{2} - | a | = 12$
$\frac{| c |^{2}}{2} + | a | = 30$
$| a \times b + c \times a | = 48 \sqrt{3}$
$a . b = - 72$

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Q. If

\to x \times \to y = \to a, \to y \times \to z = \to b, \to x \cdot \to b = γ, \to x \cdot \to y = 1

and

\to y \cdot \to z = 1

. Vector

\to x

$\frac{1}{| \to a \times \to b |^{2}} [\to a \times (\to a \times \to b)]$
$\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b - \to a \times (\to a \times \to b)]$
$\frac{γ}{| \to a \times \to b |^{2}} [\to a \times \to b + \to b \times (\to a \times \to b)]$
None of these

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Q. Which of the following unit vector is coplanar with vectors

\to A = 2 ˆ i - 3 ˆ j + ˆ k and \to B = 3 ˆ i - ˆ j - 3 ˆ k

and orthogonal to the vector

\to C = 8 ˆ i - 5 ˆ j + 2 ˆ k

$- \frac{145 ˆ i - 102 ˆ j + 122 ˆ k}{\sqrt{{(145)}^{2} - {(102)}^{2} + {(122)}^{2}}}$
$\frac{53 ˆ i + 36 ˆ j - 122 ˆ k}{\sqrt{18989}}$
$\frac{145 ˆ i - 102 ˆ j + 122 ˆ k}{\sqrt{{(145)}^{2} - {(102)}^{2} + {(122)}^{2}}}$
$- \frac{53 ˆ i + 36 ˆ j - 122 ˆ k}{\sqrt{18989}}$

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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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