Question

If `overlinea = hati - 2hatj + 3hatk, overlineb = 2hati + 3hatj - 4hatk` and `overlinec = 4hati + 13hatj - 18hatk` and `overlinec = poverlinea + qoverlineb` then p + q is equal to ______ 

Options

• 1

• -1

• 2

• -2

Answer 1

If `overlinea = hati - 2hatj + 3hatk, overlineb = 2hati + 3hatj - 4hatk` and `overlinec = 4hati + 13hatj - 18hatk` and `overlinec = poverlinea + qoverlineb` then p + q is equal to 1.

Explanation:

`overlinec = poverlinea + qoverlineb` 

∴ `4hati + 13hatj - 18hatk = p(hati - 2hatj + 3hatk) + q(2hati + 3hatj - 4hatk)` 

Comparing the co-efficients of `hati` and `hatj`, we get

p + 2q = 4

-2p + 3q = 13

Solving the above equations, we get

p = -2, q = 3

∴ p + q = 1