Question

Let = [

1 2

3 6

] = [

2 3

−1 0

]. Find

2 − −

2​

Answer 1

a+2b+2c=72a+3b+6c=133a+4b+12c=k

⇒a+2b+2c=3k...(1)2a+3b+6c=7k....(2)3a+4b+12c=13k....(3)

Eliminating a from (1) and (2), we get 

b−2c=−k....(3)

Similarly, eliminating a from (1) and (3), we get

2b−6c=−4k...(4)

From (3) and (4), we get b=c=k...(5)

Using the above value in (1) we get a=−k....(6)

From (5) and (6), a:b:c=−1:1:1

Also, a2+b2+c2=1⇒k=±31

Hence, direction cosines are (−31,31

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