The number of vector of unit length perpendicular to plane of vector a=(1,1,0) and b=(0,1,1) is/are

Question

The number of vector of unit length perpendicular to plane of vector a=(1,1,0) and b=(0,1,1) is/are (A) one (B) two (C) three (D) infinite

Tardigrade Admin · Accepted Answer

We have the equation Ax2+2Bxy+Hy2=0 ...(i) Since, the lines represented by Eq. (i) are perpendicular, therefore coefficient of x2+ coefficient of y2=0 ⇒ A+H=0 which is the required condition.

Q. The number of vector of unit length perpendicular to plane of vector $a = (1, 1, 0)$ and $b = (0, 1, 1)$ is/are

one

two

three

infinite

We have the equation $A x^{2} + 2 B x y + H y^{2} = 0$ ...(i) Since, the lines represented by Eq. (i) are perpendicular, therefore coefficient of $x^{2} +$ coefficient of $y^{2} = 0$ $\Rightarrow$ $A + H = 0$ which is the required condition.

Q. The number of vector of unit length perpendicular to plane of vector a=(1,1,0) and b=(0,1,1) is/are

one

two

three

infinite

We have the equation Ax2+2Bxy+Hy2=0 ...(i) Since, the lines represented by Eq. (i) are perpendicular, therefore coefficient of x2+ coefficient of y2=0 ⇒ A+H=0 which is the required condition.

Q. The number of vector of unit length perpendicular to plane of vector $a = (1, 1, 0)$ and $b = (0, 1, 1)$ is/are

We have the equation $A x^{2} + 2 B x y + H y^{2} = 0$ ...(i) Since, the lines represented by Eq. (i) are perpendicular, therefore coefficient of $x^{2} +$ coefficient of $y^{2} = 0$ $\Rightarrow$ $A + H = 0$ which is the required condition.