Figure shows the orientation of two vectors u and v in the XY plane. If $u=a \hat{i}+b \hat{j}$ and $v=p \hat{i}+q \hat{j} \quad$ which of the following is correct? a) $a$ and $p$ are positive while $b$ and $q$ are negative b) $a , p$, and $b$ are positive while $q$ is negative c) $a , q$, and $b$ are positive while $p$ is negative d) $a, b, p$, and $q$ are all positive

Home » Figure shows the orientation of two vectors u and v in the XY plane. If and which of the following is correct? a) and are positive while and are negative b) , and are positive while is negative c) , and are positive while is negative d) , and are all positive

Figure shows the orientation of two vectors u and v in the XY plane. If $u=a \hat{i}+b \hat{j}$ and $v=p \hat{i}+q \hat{j} \quad$ which of the following is correct? a) $a$ and $p$ are positive while $b$ and $q$ are negative b) $a , p$ , and $b$ are positive while $q$ is negative c) $a , q$ , and $b$ are positive while $p$ is negative d) $a, b, p$ , and $q$ are all positive

CBSE | Class 11 | Motion in a Plane | NCERT | Physics

Figure shows the orientation of two vectors u and v in the XY plane. If $u=a \hat{i}+b \hat{j}$ and $v=p \hat{i}+q \hat{j} \quad$ which of the following is correct? a) $a$ and $p$ are positive while $b$ and $q$ are negative b) $a , p$ , and $b$ are positive while $q$ is negative c) $a , q$ , and $b$ are positive while $p$ is negative d) $a, b, p$ , and $q$ are all positive

Answer: B)

The tail is at the origin, and the x- and y-components are projected on the positive x- and y-axes. So a and b are yes. Now translate v so that its orientation is unaltered and its tail is at the origin. The x-component has a positive x-axis projection, while the y-component has a negative y-axis projection. So q is negative while p is positive.
So, B is the right response.

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