Question

The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vec"r" = 5hat"i" - 4hat"j" + 6hat"k" + lambda(3hat"i" + 7hat"j" + 2hat"k")`.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

The Cartesian form of the equation is `(x - 5)/3 = (y + 4)/7 = (z - 6)/2 = lambda`

∴ Here x₁ = 5

y₁ = – 4

z₁ = 6,

a = 3

b = 7

c = 2

So, the vector equation is `vec"r" = (5hat"i" - 4hat"j" + 6hat"k") + lambda(3hat"i" + 7hat"j" + 2hat"k")`