If x-c-y-a and y-c-x-b- where c is a non - zero vector- then which of the following is correct

Given: x+c×y=a⋯(i) y+c×x=b⋯(ii) Taking cross with c, of equation (ii) We have c×y+c× (c×x)=c×b Now, using (i), we have ⇒ (a x)+ (c·x)c (c·c)x=c×b ⋯(iii) nbs ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Work Done as Dot Product

If x+c×y=a an...

Question

If $\to x + \to c \times \to y = \to a$ and $\to y + \to c \times \to x = \to b$ , where $\to c$ is a non - zero vector, then which of the following is correct

\to x = \frac{(\to b \times \to c) + \to a + (\to c \cdot \to a) \to c}{1 + \to c \cdot \to c}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\to x = \frac{(\to c \times \to b) + \to b + (\to c \cdot \to a) \to c}{1 + \to c \cdot \to c}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to x = \frac{(\to a \times \to c) + \to b + (\to c \cdot \to a) \to c}{1 + \to c \cdot \to c}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to x = \frac{(\to a \times \to c) + \to b + (\to c \cdot \to a) \to c}{1 - \to c \cdot \to c}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\to x = \frac{(\to b \times \to c) + \to a + (\to c \cdot \to a) \to c}{1 + \to c \cdot \to c}$
Given:
$\to x + \to c \times \to y = \to a \dots (i) \to y + \to c \times \to x = \to b \dots (i i)$
Taking cross with $\to c,$ of equation $(i i)$ We have $\to c \times \to y + \to c \times (\to c \times \to x) = \to c \times \to b$
Now, using $(i),$ we have
$\Rightarrow (\to a - \to x) + (\to c \cdot \to x) \to c - (\to c \cdot \to c) \to x = \to c \times \to b \dots (i i i)$

Also taking dot product with $\to c$ in equation $(i),$ we have
$\Rightarrow \to c \cdot \to x + \to c \cdot (\to c \times \to y) = \to c \cdot \to a$ or $\to c \cdot \to x + 0 = \to c \cdot \to a$ or $\to c \cdot \to x = \to c \cdot \to a \dots (i v)$

Using $(i v)$ in $(i i i),$ we have
$\Rightarrow (\to a - \to x) + (\to c \cdot \to a) \to c - (\to c \cdot \to c) \to x = \to c \times \to b$
$\Rightarrow \to x (1 + (\to c \cdot \to c)) = \to b \times \to c + \to a + (\to c \cdot \to a) \cdot \to c$
$\Rightarrow \to x = \frac{(\to b \times \to c) + \to a + (\to c \cdot \to a) \cdot \to c}{1 + \to c \cdot \to c}$

Suggest Corrections

Similar questions

Q. If

a + x = b + y = c + z + 1

, where

a, b, c, x, y, z

are non-zero distinct real numbers, then

∣ ∣ ∣ ∣ \begin{matrix} x & a + y & x + a y & b + y & y + b z & c + y & z + c \end{matrix} ∣ ∣ ∣ ∣

is equal to:

Q. If

x, y, z \in R^{+}

and

a, b, c

are non-zero such that

∣ ∣ ∣ ∣ \begin{matrix} a x & c y & b z b y & a z & c x c z & b x & a y \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a x & b x & c x c y & a y & b y b z & c z & a z \end{matrix} ∣ ∣ ∣ ∣,

then which of the following is/are correct?

Q. If

\to x, \to y

are two non-zero and non-collinear vectors satisfying

[(a - 2) α^{2} + (b - 3) α + c] \to x + [(a - 2) β^{2} + (b - 3) β + c] \to y + [(a - 2) γ^{2} + (b - 3) γ + c] (\to x \times \to y) = \to 0,

where

α, β, γ

are three distinct real numbers, then which of the following statement(s) is/are correct ?

Q. If

\frac{x y}{x + y} = a, \frac{x z}{x + z} = b

and

\frac{y z}{y + z} = c

where a, b, c are all non - zero numbers, then x equals to :

Q. If

¯ ¯ ¯ a, ¯ ¯ b

and

¯ ¯ c

are non-coplanar vectors and If

¯ ¯ ¯ d

is such that

¯ ¯ ¯ d = \frac{1}{x} (¯ ¯ ¯ a + ¯ ¯ b + ¯ ¯ c)

and

¯ ¯ ¯ a = \frac{1}{y} (¯ ¯ b + ¯ ¯ c + ¯ ¯ ¯ d)

where x and y are non-zero real numbers, then

\frac{1}{x y} (¯ ¯ ¯ a + ¯ ¯ b + ¯ ¯ c + ¯ ¯ ¯ d) =

Join BYJU'S Learning Program

If →x+→c×→y=→a and →y+→c×→x=→b, where →c is a non - zero vector, then which of the following is correct

If $\to x + \to c \times \to y = \to a$ and $\to y + \to c \times \to x = \to b$ , where $\to c$ is a non - zero vector, then which of the following is correct