Question

If a = i - j , b = i+j+k and c be a vector such that a x c + b = o and a.c= 4, then IcI

2

is equal to____.​

Answer 1

| c |² = 9.5

Step-by-step explanation:

Given a = i - j, b = i + j + k

Let the vector c be (x i + y j + z k)

Now, a × c

| i j k |

= | 1 - 1 0 |

| x y z |

= (- z) i + (- z) j + (x + y) k

Given that,

a × c + b = 0

or, (- z) i + (- z) j + (x + y) k + i + j + k = 0

or, (1 - z) i + (1 - z) j + (1 + x + y) k = 0

Equating the coefficients of i, j, k from both sides, we get

1 - z = 0 or, z = 1

1 - z = 0 or, z = 1

1 + x + y = 0 ..... (1)

Again,

a . c = 4

or, (i - j) . (x i + y j + z k) = 4

or, x - y = 4

or, x = y + 4 .... (2)

From (1) and (2), we get

1 + y + 4 + y = 0

or, 2y + 5 = 0

or, y = - 5/2

From (2), we get

x = - 5/2 + 4

= (- 5 + 8)/2

= 3/2

i.e., x = 3/2

Therefore, c = 3/2 i - 5/2 j + k

Then | c |² = (3/2)² + (- 5/2)² + 1²

= 9/4 + 25/4 + 1

= (9 + 25 + 4)/4

= 38/4

= 9.5