बिंदुओं `(-1, 0, 2 )` और `(3, 4, 6) ` से होकर जाने वाली रेखा का सदिश समीकरण ज्ञात कीजिए |

Options

A. ` - hati + 2hatk + lamda ( 4 hati + 4 hatj + 4 hatk ) `
B. ` 2 hati - hatk + lamda (4 hati + 4hatj + 4 hatk ) `
C. ` - hati + 2 hatk + lamda ( - hati + 4hatj + 2hatk ) `
D. ` - hati + 2 hatk + lamda ( 3 hati + 4hatj + 6 hatk ) `

Answer

A

Explanation

Let a and b be the position vectors of the point ` A ( - 1 , 0 , 2 ) and B ( 3, 4 , 6 ) `
Then, ` a= - hati + 2 hatk and b = 3 hati + 4hatj + 6 hatk `
Let r be the position vector of any point on the line.
Then the vector equation of the line is
` r = - hati + 2 hatk + lamda ( 4hati + 4hatj + 4 hatk ) `