The direction cosines of a line passing through two points P(x1, y1, z1) and Q(x2, y2, z2) are

Question

The direction cosines of a line passing through two points P(x1, y1, z1) and Q(x2, y2, z2) are (A) (x2 - x1), (y2 - y1), (z2 - z1) (B) (x2 + x1), (y2 + y1), (z2 + z1) (C) (x2-x1/PQ), (y2-y1/PQ), (z2-z1/PQ) (D) (x2+x1/PQ), (y2+y1/PQ), (z2+z1/PQ)

Tardigrade Admin · Accepted Answer

P(x1, y1, z1) and Q(x2, y2, z2) ∴ Direction ratios of line PQ=(x2-x1, y2-y1, z2-z1) ⇒ direction cosine of PQ = [(x2-x1/√(x2-x1)2+(y2-y1)2+(z2-z1)2), (y2-y1/√(x2-x1)2+(y2-y1)2+(z2-z1)2), (z2-z1/√(x2-x1)2+(y2-y1)2+(z2-z1)2)] =[(x2-x1/PQ), (y2-y1/PQ), (z2-z1/PQ)] where PQ=√(x2-x1)2+(y2-y1)2+(z2-z1)2

Q. The direction cosines of a line passing through two points $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$ are

$(x_{2} - x_{1})$ , $(y_{2} - y_{1})$ , $(z_{2} - z_{1})$

$(x_{2} + x_{1})$ , $(y_{2} + y_{1})$ , $(z_{2} + z_{1})$

$\frac{x _{2} - x _{1}}{PQ}$ , $\frac{y _{2} - y _{1}}{PQ}$ , $\frac{z _{2} - z _{1}}{PQ}$

$\frac{x _{2} + x _{1}}{PQ}$ , $\frac{y _{2} + y _{1}}{PQ}$ , $\frac{z _{2} + z _{1}}{PQ}$

Q. The direction cosines of a line passing through two points P(x1​,y1​,z1​) and Q(x2​,y2​,z2​) are

(x2​−x1​), (y2​−y1​), (z2​−z1​)

(x2​+x1​), (y2​+y1​), (z2​+z1​)

PQx2​−x1​​, PQy2​−y1​​, PQz2​−z1​​

PQx2​+x1​​, PQy2​+y1​​, PQz2​+z1​​

Q. The direction cosines of a line passing through two points $P (x_{1}, y_{1}, z_{1})$ and $Q (x_{2}, y_{2}, z_{2})$ are

$(x_{2} - x_{1})$ , $(y_{2} - y_{1})$ , $(z_{2} - z_{1})$

$(x_{2} + x_{1})$ , $(y_{2} + y_{1})$ , $(z_{2} + z_{1})$

$\frac{x _{2} - x _{1}}{PQ}$ , $\frac{y _{2} - y _{1}}{PQ}$ , $\frac{z _{2} - z _{1}}{PQ}$

$\frac{x _{2} + x _{1}}{PQ}$ , $\frac{y _{2} + y _{1}}{PQ}$ , $\frac{z _{2} + z _{1}}{PQ}$