Applications ...

Applications of Cross Product

Trending Questions

Q. If

x . a = 0, x \times b = c \times b

then x =

$c - \frac{c . a}{b . a} b$
$c - \frac{c . a}{b . a} a$
$a - \frac{c . a}{b . a} b$
$b - \frac{c . a}{b . a} b$

View Solution

Q. If

\to a, \to b

and

\to c

be three non-zero and coplanar vectors, then which of the following statement(s) is/are true?

$\to a \times (\to b \times \to c), \to b \times (\to c \times \to a), \to c \times (\to a \times \to b$ form a right handed system
$\to c, (\to a \times \to b) \times \to c, \to a \times \to b$ form a right handed system
$\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a < 0$ if $\to a + \to b + \to c = 0$
$\frac{(\to a \times \to b) \cdot (\to b \times \to c)}{(\to b \times \to c) \cdot (\to a \times \to c)} = - 1$ if $\to a + \to b + \to c = 0$

View Solution

Q. Vectors

\to A

and

\to B

satisfying the vector equation

\to A + \to B = \to a, \to A \times \to B = \to b

and

\to A \cdot \to a = 1

, where

\to a

and

\to b

are given vectors, are

$\to A = \frac{(\to a \times \to b) - \to a}{| \to a |^{2}}$
$\to B = \frac{(\to b \times \to a) + \to a (| \to a |^{2} - 1)}{| \to a |^{2}}$
$\to A = \frac{(\to a \times \to b) + \to a}{| \to a |^{2}}$
$\to B = \frac{(\to b \times \to a) - \to a (| \to a |^{2} - 1)}{| \to a |^{2}}$

View Solution

Q. The value of b such that the scalar product of the vector

^i +^j +^k

with the unit vector parallel to the sum of the vectors

2^i + 4^j + 5^k

and

b^i + 2^j + 3^k

is one, is

-2
-1
\N
1

View Solution

Q. A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points

^i - 2^j + 3^k, 2^i - 3^j + 4^k

and

^i - 5^j + 7^k

Also makes and obtuse angle with y - axis
Also makes an obtuse angle with z - axis
Also makes an obtuse angle with y and z axis
None of the above

View Solution

Q. If

2^i + 3^j + 4^k

and

^i -^j +^k

are two adjacent sides of a parallelogram, then the area of the parallelogram will be

$\sqrt{87}$
$\sqrt{70}$
Cannot be calculated from the given data
none of the above

View Solution

Q. If

\to a =^i +^j -^k,

\to b =^i -^j +^k

and

\to c

is a unit vector perpendicular to the vector

\to a

and coplanar with

\to a

and

\to b,

then direction cosines of a vector which is perpendicular to both

\to a

and

\to c

are

$(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$
$(\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}})$
$(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)$
$(- \frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}})$

View Solution

Q. The vector area of the triangle with vertices

^i +^j +^k,^i +^j + 2^k,^i + 2^j +^k

$^i$
$-^i$
$\frac{1}{2} i$
$- \frac{1}{2} i$

View Solution

Q. A force of 500 N is applied to a wrench as shown in the figure. The force is being applied at an angle of

235^{\circ}

with positive x – axis

The length of the wrench is 0.3 m The magnitude of vector moment of the force F acting at A about origin is given by _____ and the screw at origin will move in ____ direction.

$500 \times 0.3 \times s i n 235^{\circ}$ negative z direction
$500 \times 0.3 \times s i n 55^{\circ}$ positive z direction
$500 \times 0.3 \times s i n 125^{\circ}$ negative z direction
$500 \times 0.3 \times s i n 135^{\circ}$ positive z direction

View Solution

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

$\frac{1}{2} (^i +^j +^k)$
$2 (^i +^j +^k)$
$2 (-^i +^j +^k)$
$\frac{1}{2} (^i -^j +^k)$

View Solution

Q. If a is any vector then

(a \times^i)^{2} + (a \times^j)^{2} + (a \times^k)^{2}

$a^{2}$
$2 a^{2}$
$3 a^{2}$
$4 a^{2}$

View Solution

Q. If

\to a

and

\to b

are unequal vectors such that

(\to a - \to b) \times [(\to b + \to a) \times (2 \to a + \to b)] = \to a + \to b

, then the angle

θ

between

\to a

and

\to b

$0$
$\frac{π}{2}$
$\frac{π}{4}$
$π$

View Solution

Q. If the vectors

\to a, \to b

and

\to c

form the sides BC, CA and AB respectively of a

Δ A B C

, then

$\to a . \to b + \to b . \to c + \to c . \to a = 0$
$\to a \times \to b = \to b \times \to c = \to c \times \to a$
$\to a . \to b = \to b . \to c = \to c . \to a$
$\to a \times \to b + \to b \times \to c = \to c \times \to a = \to 0$

View Solution

Q. The area of the parallelogram whose diagonals are

^i - 3^j + 2^k, -^i + 2^j

$4 \sqrt{29} s q$ .units
$\frac{1}{2} \sqrt{21} s q$ .units
$10 \sqrt{3} s q$ .units
$\frac{1}{2} \sqrt{270} s q$ .units

View Solution

Q. If

\to a

and

\to b

are the two sides of a triangle, then the area of triangle will be given by

| \to a \times \to b |

True
False

View Solution

Q. In a

△ A B C, A B = r i + j, A C = s i - j

if the area of triangle is of unit magnitude, then

$| r - s | = 2$
$| r + s | = 1$
$| r + s | = 2$
$| r - s | = 1$

View Solution

Q. A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points

^i - 2^j + 3^k, 2^i - 3^j + 4^k

and

^i - 5^j + 7^k

Also makes and obtuse angle with y - axis
Also makes an obtuse angle with z - axis
Also makes an obtuse angle with y and z axis
None of the above

View Solution

Q. If

\to a

and

\to b

are the two sides of a triangle, then the area of triangle will be given by

| \to a \times \to b |

True
False

View Solution