Cross Product...

Cross Product of Two Vectors

Trending Questions

Q. Sum of coefficients of

ˆ i, ˆ j

and

ˆ k

in the cross product

(2 ˆ i + 3 ˆ j + 4 ˆ k)

\times

(ˆ i - ˆ j + ˆ k)

will be___.

$I f \to u = \to a - \to b a n d \to v = \to a + \to b a n d | \to a | = | \to b | = 2, t h e n | \to u \times \to v | =$

Q. Let

\to a = 2^i +^j - 2^k a n d \to b =^i +^j .

\to c

is a vector such that

\to a . \to c = | \to c |, | \to c - \to a | = 2 \sqrt{2}

and the angle between

(\to a \times \to b) a n d \to c i s 30^{\circ}, t h e n | (\to a \times \to b) \times \to c |

is equal to

\to a \neq 0, \to a \times \to b = \to a \times \to c \Rightarrow \to b = \to c

Q. A unit vector perpendicular to the plane determined by the points P(1, -1, 2), Q(2, 0, -1) and R(0, 2, 1) is

Q. A unit vector perpendicular to the plane of

a = 2^i - 6^j - 3^k, b = 4^i + 3^j -^k

If $\to a \times \to b = \to c, \to b \times \to c = \to a$ and a, b, c be the moduli of the vectors $\to a, \to b, \to c$ respectively, then

The scalars l and m such that $l \to a + m \to b = \to c$ where $\to a, \to b$ and $\to c$ are given vectors, are equal to

$l = \frac{(\to c \times \to b) . (\to a \times \to b)}{| \to a \times \to b |^{2}}$ ; $m = \frac{(\to c \times \to a) . (\to b \times \to a)}{| \to b \times \to a |^{2}}$
$l = \frac{(\to c \times \to b) . (\to a \times \to b)}{| \to a \times \to b |}$ ; $m = \frac{(\to c \times \to a) . (\to b \times \to a)}{| \to b \times \to a |}$
$l = \frac{| \to c \times \to b |^{2}}{| \to a \times \to b |^{2}}$ ; $m = \frac{| \to c \times \to a |^{2}}{| \to b \times \to a |^{2}}$
$l = \frac{| \to c \times \to a |^{2}}{| \to b \times \to a |^{2}}$ ; $m = \frac{| \to c \times \to b |^{2}}{| \to a \times \to b |^{2}}$

Q. If 3 vectors

¯ ¯ ¯ a . ¯ ¯ b, ¯ ¯ c

all lie in one plane (i.e., they are coplanar) then

¯ ¯ c

(¯ ¯ ¯ a \times ¯ ¯ b)

= _______

___

The point of intersection of the lines $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$ is