The value of $c$ so that for all real $x$, then vectors o$cx\;\widehat {\bf{i}} - 6\widehat {\bf{j}} + 3{\bf{\hat k}},\;x\widehat {\bf{i}} + 2\widehat {\bf{j}} + 2cx{\bf{\hat k}}$ make an obtuse angle are

JEE MATHEMATICS MCQ: DOT PRODUCT OF VECTORS

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Application +4 | -1

The value of

c

so that for all real

x

, then vectors o

cx\;\widehat \mathbf{i} - 6\widehat \mathbf{j} + 3\mathbf{\hat k},\;x\widehat \mathbf{i} + 2\widehat \mathbf{j} + 2cx\mathbf{\hat k}

make an obtuse angle are

View answer and explanation

Correct option: C

- \frac{4}{3} < c < 0

Option C (

- \frac{4}{3} < c < 0

) is correct because for the angle to be obtuse, the dot product must be negative, leading to a quadratic inequality whose solution gives the range of c.

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