Question

Two vectors A bar and B bar lie in one plane < vector C bar lies in different plane . Then A bar +B bar+ C bar

Answer 1

Correct Question -

Two vectors $\vec{A}$ and $\vec{B}$ lie in one plane. $\vec{C}$ lies in different plane.

Then $\vec{A} + \vec{B} + \vec{C}$

Answer -

Can never be zero

Explanation -

$\longrightarrow$The sum of only co - planar vectors can be zero.

$\longrightarrow$Here , the 2 vectors are in same plane and 1 is non co planar. So these three vectors are non - co planar.

$\longrightarrow$ Sum of non - co planar vectors can never be zero.

$\longrightarrow$So the sum of these 3 vectors can never be zero.

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Additional information -

R = $\sqrt{{a}^{2} + {b}^{2} + 2ab \cos\theta }$

R $\longrightarrow$ magnitude of resultant vector $\vec{R}$

A $\longrightarrow$ magnitude of vector $\vec{A}$

B $\longrightarrow$ magnitude of vector $\vec{B}$

$\theta$ $\longrightarrow$ angle b/w $\vec{A}$ and $\vec{B}$

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$tan \phi = \frac{b sin}{a + bcos \theta}$

$\phi$$\longrightarrow$ angle of $\vec{R}$ from $\vec{A}$

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Thanks