If ${\bf{\vec a}},{\bf{\vec b}},{\bf{\vec c}}$ are the unit vectors such that ${{\bf{\vec a}}}$ is perpendicular to the plane ${\bf{\vec b}},{\bf{\vec c}}$ and the angle between ${\bf{\vec b}},{\bf{\vec c}}$ is $\frac{\pi }{3}$ then $\left| {{\bf{\vec a}} + {\bf{\vec b}} + {\bf{\vec c}}} \right|$ is equal to

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

1 Easy

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Application +4 | -1

\mathbf{\vec a},\mathbf{\vec b},\mathbf{\vec c}

are the unit vectors such that

{\mathbf{\vec a}}

is perpendicular to the plane

\mathbf{\vec b},\mathbf{\vec c}

and the angle between

\mathbf{\vec b},\mathbf{\vec c}

\frac{\pi }{3}

then

\left| {\mathbf{\vec a} + \mathbf{\vec b} + \mathbf{\vec c}} \right|

is equal to

View answer and explanation

Correct option: C

\mathrm{\;} \pm 2

Option C ( ± 2) is correct because it calculates the magnitude of the vector sum of three unit vectors, where one is perpendicular to the plane of the other two.

More Questions from DOT PRODUCT OF VECTORS

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The distance between the planes given by

\mathbf{r} .(\mathbf{i}+2 \mathbf{j}-2 \mathbf{k})+5=0

and

\mathbf{r}-(\mathbf{i}+2 \mathbf{j}-2 \mathbf{k})-8=0

is A vector which makes equal angles with the vectors

\frac{1}{3}\left( {\hat i - 2\hat j + 2\hat k} \right),\frac{1}{5}\left( { - 4\hat i - 3\hat k} \right)

, and

{\hat j}

, is If vector

\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}

and vector

\mathbf{b}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}

, then

\frac{\text { Projection of vector } \mathbf{a} \text { on vector } \mathbf{b}}{\text { Projection of vector } \mathbf{b} \text { on vector } \mathbf{a}}

is equal to The angle between

{\mathbf{\vec a}}

and

{\mathbf{\vec b}}

\frac{{5\pi }}{6}

and the projection of

{\mathbf{\vec a}}

in the direction of

{\mathbf{\vec b}}

\frac{{ - 6}}{{\sqrt 3 }}

then

\left| {\mathbf{\vec a}} \right|

is equal to A velocity

\frac{1}{4} \mathrm{~m} / \mathrm{s}

is resolved into two components along

O A

and

O B

making angles

30^{\circ}

and

45^{\circ}

respectively with the given velocity. Then the component along

O B

is Find the equation of the perpendicular drown from the origin to the plane

2x + 4y - 5z = 10