Question

Component of 3i+4j perpendicular to I+j and in the same plane as that of 3i+4j is

Answer 1

Answer:

The cardinal vector is (3i + 4j + 0k). There is nothing along Z-axis. So, this vector lies in xy plane with z = 0.

The other vector (1i + 1j + 0k) also lies in the same plane. Suppose, vector (ai + bj) be a coplanar vector perpendicular to it. So, dot product of (1i + 1j + 0k) and (ai + bj) shall be zero.

|a * 1 + b * 1| = 0

|a + b| = 0

b = - a.

So, we have to find out component of the vector (3i + 4j) along (ai - aj).

Unit vector along (ai - aj) = (ai - aj) / √(2a^2) = {(1 / √2)i - (1 / √2)j}

Component of (3i + 4j) along (ai - aj)

= Dot product of (3i + 4j) and {(1 / √2)i - (1 / √2)j}

= |3 * (1 / √2) - 4 * (1 / √2)|

= |- (1 / √2)|

= (1 / √2).