Question

Given the vectors a = i + j - 2k , b = i + 2j – k , c = i + j + k Find (3a - 2b) x 3c

Answer 1

Answer:

c is coplanar with a and b.

∴c=xa+yb

⇒c=x(2i+j+k)+y(i+2j−k)

⇒c=(2x+y)i+(x+2y)j+(x−y)k

a.c=0

∴2(2x+y)+x+2y+x−y=0

⇒y=−2x

c=−3xj+3xk=3x(−j+k)

∣c∣=1

∴9x

2

+9x

2

=1

⇒x=±

3

2

1

⇒c=

2

1

(−j+k).

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