Advertisements
Advertisements
प्रश्न
If `veca ` and `vecb` are two unit vectors such that `veca+vecb` is also a unit vector, then find the angle between `veca` and `vecb`
Advertisements
उत्तर
Given: `veca` and `vec b` are unit vectors
`therefore |veca|=|vecb|=1`
Let the angle between ` veca and vecb "be " theta`
It is given that, `(veca+vecb)` is a unit vector
`therefore |veca+vecb|=1`
`(veca+vecb)(veca+vecb)=1`
`|veca|^2+2veca.vecb+|vecb|^2=1`
`|veca|^2+2|veca|.|vecb|+|vecb|^2=1`
`1+2xx1xx1xxcostheta+1=1`
`2costheta=-1`
`cos theta=-1/2`
`therefore theta=(2pi)/3`
APPEARS IN
संबंधित प्रश्न
Vectors `veca,vecb and vecc ` are such that `veca+vecb+vecc=0 and |veca| =3,|vecb|=5 and |vecc|=7 ` Find the angle between `veca and vecb`
If `veca and vecb` are two vectors such that `|veca+vecb|=|veca|,` then prove that vector `2veca+vecb` is perpendicular to vector `vecb`
Show that the vectors `veca, vecb` are coplanar if `veca+vecb, vecb+vecc ` are coplanar.
If `vec a, vec b, vec c` are unit vectors such that `veca+vecb+vecc=0`, then write the value of `vec a.vecb+vecb.vecc+vecc.vec a`.
If `vec a=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk` , then find the projection of `vec a and vecb`
The scalar product of the vector `veca=hati+hatj+hatk` with a unit vector along the sum of vectors `vecb=2hati+4hatj−5hatk and vecc=λhati+2hatj+3hatk` is equal to one. Find the value of λ and hence, find the unit vector along `vecb +vecc`
Prove that `(veca + vecb).(veca + vecb)` = `|veca|^2 + |vecb|^2` if and only if `veca . vecb` are perpendicular, given `veca != vec0, vecb != vec0.`
Find \[\vec{a} \cdot \vec{b}\] when
\[\vec{a} = \hat{j} - \hat{k} \text{ and } \vec{b} = 2 \hat{i} + 3 \hat{j} - 2 \hat{k}\]
For what value of λ are the vectors \[\vec{a} \text{ and } \vec{b}\] perpendicular to each other if
\[\vec{a} = 2 \hat{i} + 3 \hat{j} + 4\hat{k} \text{ and } \vec{b} = 3 \hat{i} - 2 \hat{j} +\lambda \hat{k}\]
What is the angle between vectors \[\vec{a} \text{ and } \vec{b}\] with magnitudes 2 and \[\sqrt{3}\] respectively? Given \[\vec{a} . \vec{b} = \sqrt{3} .\]
Find the cosine of the angle between the vectors \[4 \hat{i} - 3 \hat{j} + 3 \hat{k} \text{ and } 2 \hat{i} - \hat{j} - \hat{k} .\]
If \[\vec{a} \text{ and } \vec{b}\] are vectors of equal magnitude, write the value of \[\left( \vec{a} + \vec{b} \right) . \left( \vec{a} - \vec{b} \right) .\]
If \[\vec{a} \text{ and } \vec{b}\] are two vectors of the same magnitude inclined at an angle of 60° such that \[\vec{a} . \vec{b} = 8,\] write the value of their magnitude.
If \[\hat{a} , \hat{b}\] are unit vectors such that \[\hat{a} + \hat{b}\] is a unit vector, write the value of \[\left| \hat{a} - \hat{b} \right| .\]
Write the projections of \[\vec{r} = 3 \hat{i} - 4 \hat{j} + 12 \hat{k}\] on the coordinate axes.
If \[\vec{a} \text{ and } \vec{b}\] are unit vectors, find the angle between \[\vec{a} + \vec{b} \text{ and } \vec{a} - \vec{b} .\]
For what value of λ are the vectors \[\vec{a} = 2 \hat{i} + \lambda \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}\] perpendicular to each other?
Find the projection of \[\vec{a} \text{ on } \vec{b} \text{ if } \vec{a} \cdot \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} .\]
Write the value of p for which \[\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} \text{ and } \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k}\] are parallel vectors .
Find the value of λ if the vectors \[2 \hat{i} + \lambda \hat{j} + 3 \hat{k} \text{ and } 3 \hat{i} + 2 \hat{j} - 4 \hat{k}\] are perpendicular to each other.
If \[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 3 \text{ and } \vec{a} \cdot \vec{b} = 3,\] find the projection of \[\vec{b} \text{ on } \vec{a}\]
Find λ when the projection of \[\vec{a} = \lambda \hat{i} + \hat{j} + 4 \hat{k} \text{ on } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k}\] is 4 units.
Write the projection of \[\vec{b} + \vec{c} \text{ on } \vec{a} \text{ when } \vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k} , \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} \text{ and } \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .\]
If \[\vec{a}\] and \[\vec{b}\] are two unit vectors such that \[\vec{a} + \vec{b}\] is also a unit vector, then find the angle between \[\vec{a}\] and \[\vec{b}\]
If `θ` be the angle between any two vectors `veca` and `vecb`, then `|veca * vecb| = |veca xx vecb|`, when `θ` is equal to
If the two vectors `3hati + αhatj + hatk` and `2hati - hatj + 8hatk` are perpendicular to each other, then find the value of α.
