Projection of line segment joining (.2,3,4.) and (.5,6,7.) on plane 2x+y+z=1 is :

Question

Projection of line segment joining (.2,3,4.) and (.5,6,7.) on plane 2x+y+z=1 is : (A) 2 (B) √3 (C) 3 (D) 3√3

Tardigrade Admin · Accepted Answer

Let A≡ (.2,3,4.) and B=(.5,6,7.). Then AB=3√3 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-exalkmtichwbyjxq.jpg" /> Plane: 2x+y+z=1 Projection of overset arrow A B on vector 2 hati+ hatj+ hatk which is normal to plane, BC=((. 3 hati + 3 hatj + 3 hatk .) ⋅ (. 2 hati + hatj + hatk .)/√6)=(12/√6)=2√6 ∴ Projection of overset arrow A B on plane A C=√(3 √3-(2 √6=√3

Q. Projection of line segment joining $(2, 3, 4)$ and $(5, 6, 7)$ on plane $2 x + y + z = 1$ is :

$2$

$3$

$3$

$33$

Q. Projection of line segment joining (2,3,4) and (5,6,7) on plane 2x+y+z=1 is :

2

3​

3

33​

Let A≡(2,3,4) and B=(5,6,7). Then AB=33​ Plane: 2x+y+z=1 Projection of AB→ on vector 2i^+j^​+k^ which is normal to plane, BC=6​(3i^+3j^​+3k^)⋅(2i^+j^​+k^)​=6​12​=26​ ∴ Projection of AB→ on plane AC=(33​−(26​​=3​

Q. Projection of line segment joining $(2, 3, 4)$ and $(5, 6, 7)$ on plane $2 x + y + z = 1$ is :

$2$

$3$

$3$

$33$