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

Applications of Dot Product

Calculate the...

Question

Calculate the scalar product of the following vectors.
Find the vector c being given that it is perpendicular to the vectors $a = {2, 3, - 1}, b = {1, - 2, 3}$ and satisfies the condition $c . {2 i - j + k} = - 6.$

Open in App

Solution

Let c be a vector (x,y,z)
According to given conditions
$a . c = 2 x + 3 y - z = 0................. (1)$
$b . c = x - 2 y + 3 z = 0.................. (2)$
$c . (2 \to i - \to j + \to k) = 2 x - y + z = - 6............ (3)$
Equations $(1) - 2 \times (2)$
$\Rightarrow y = z . . . . . . . . . (4)$
Equations $3 \times (1) + (2)$
$\Rightarrow x = - y . . . . . (5)$
Substitute Equation $4 a n d 5 i n 3$
$- 2 y - y + y = - 6$
$y = 3$
Hence $\to c = (- 3, 3, 3)$

Suggest Corrections

Similar questions

b \cdot c = 3, w h e r e c = {1, - 1, 2},

a

d

a = {- 2, - 1, 1} a n d d = {3, 5, - 2} .

b = {1, - 3, 1}

a \cdot b = 22.

b = {3, 6, 6}

a . b = 27.

\to c

\to a = (2, - 3, 1), \to b = (1, - 2, 3)

\to c

(^i + 2^j - 7^k) = 10

^c

¯ c

¯ a = (2, - 3, 1)

¯ b = (1, - 2, 3)

¯ c \cdot (^i + 2^j - 7^k) = 10

¯ c

Join BYJU'S Learning Program