If the projection of the vector ${\bf{\vec a}}\;{\rm{on\;}}{\bf{\vec b}}$ is $\left| {{\bf{\vec a}} \times {\bf{\vec b}}} \right|$ and if $3{\bf{\vec b}} = \widehat {\bf{i}} + \widehat {\bf{j}} + {\bf{\hat k}}$, then the angle between ${\bf{\vec a}}{\rm{\;and\;}}{\bf{\vec b}}$ is

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Application +4 | -1

If the projection of the vector

\mathbf{\vec a}\;\mathrm{on\;}\mathbf{\vec b}

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

and if

3\mathbf{\vec b} = \widehat \mathbf{i} + \widehat \mathbf{j} + \mathbf{\hat k}

, then the angle between

\mathbf{\vec a}\mathrm{\;and\;}\mathbf{\vec b}

View answer and explanation

Correct option: A

\frac{\mathrm{\pi }}{3}

Option A (

\frac{\mathrm{\pi }}{3}

) is correct because it represents the angle between the vectors a and b, derived from the given condition and the properties of dot and cross products.

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