Advertisements
Advertisements
प्रश्न
If `veca, vecb, vecc` are three non-zero unequal vectors such that `veca.vecb = veca.vecc`, then find the angle between `veca` and `vecb - vecc`.
Advertisements
उत्तर
Given, `veca.vecb = veca.vecc`
∴ `veca.vecb - veca.vecc` = 0
`\implies veca.(vecb - vecc)` = 0
Either `vecb = vecc` or `veca ⊥ (vecb - vecc)`
But `vecb ≠ vecc`
[∵ `veca, vecb, vecc` are three non-zero unequal vectors]
∴ Angle between `veca` and `vecb - vecc` is 90°.
APPEARS IN
संबंधित प्रश्न
Find the projection of the vector `hati+3hatj+7hatk` on the vector `2hati-3hatj+6hatk`
Find `lambda` if the scalar projection of `vec a = lambda hat i + hat j + 4 hat k` on `vec b = 2hati + 6hatj + 3hatk` is 4 units
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
\[\vec{a} = \lambda \hat{i} + 2\hat{j} + \hat{k} \text{ and } \vec{b} = 5\hat{i} - 9 \hat{j} + 2\hat{k}\]
Find the cosine of the angle between the vectors \[4 \hat{i} - 3 \hat{j} + 3 \hat{k} \text{ and } 2 \hat{i} - \hat{j} - \hat{k} .\]
For any two vectors \[\vec{a} \text{ and } \vec{b}\] write when \[\left| \vec{a} + \vec{b} \right| = \left| \vec{a} - \vec{b} \right|\] holds.
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 \[\vec{b}\] is a unit vector such that\[\left( \vec{a} + \vec{b} \right) . \left( \vec{a} - \vec{b} \right) = 8, \text{ find } \left| \vec{a} \right| .\]
If \[\hat{a} , \hat{b}\] are unit vectors such that \[\hat{a} + \hat{b}\] is a unit vector, write the value of \[\left| \hat{a} - \hat{b} \right| .\]
For any two non-zero vectors, write the value of \[\frac{\left| \vec{a} + \vec{b} \right|^2 + \left| \vec{a} - \vec{b} \right|^2}{\left| \vec{a} \right|^2 + \left| \vec{b} \right|^2} .\]
Write the projection of \[\hat{i} + \hat{j} + \hat{k}\] along the vector \[\hat{j}\]
Write a vector satisfying \[\vec{a} . \hat{i} = \vec{a} . \left( \hat{i} + \hat{j} \right) = \vec{a} . \left( \hat{i} + \hat{j} + \hat{k} \right) = 1 .\]
If \[\vec{a} \text{ and } \vec{b}\] are mutually perpendicular unit vectors, write the value of \[\left| \vec{a} + \vec{b} \right| .\]
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 .
Write the angle between two vectors \[\vec{a} \text{ and } \vec{b}\] with magnitudes \[\sqrt{3}\] and 2 respectively if \[\vec{a} \cdot \vec{b} = \sqrt{6} .\]
Write the projection of the vector \[\hat{i} + 3 \hat{j} + 7 \hat{k}\] on the vector \[2 \hat{i} - 3 \hat{j} + 6 \hat{k}\]
For what value of λ are the vectors \[\vec{a} = 2 \text{i} + \lambda \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}\] perpendicular to each other?
Write the projection of the vector \[7 \hat{i} + \hat{j} - 4 \hat{k}\] on the vector \[2 \hat{i} + 6 \hat{j}+ 3 \hat{k} .\]
Write the value of λ so that the vectors \[\vec{a} = 2 \hat{i} + \lambda \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}\] are perpendicular to each other.
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 \[\vec{b}\]
Prove that, for any three vectors \[\vec{a} , \vec{b} , \vec{c}\] \[\left[ \vec{a} + \vec{b} , \vec{b} + \vec{c} , \vec{c} + \vec{a} \right] = 2 \left[ \vec{a} , \vec{b} , \vec{c} \right]\].
Let `vec("a") = hat"i" + 2hat"j" - 3hat"k"` and `vec("b") = 3hat"i" -"j" +2hat("k")` be two vectors. Show that the vectors `(vec("a")+vec("b"))` and `(vec("a")-vec("b"))`are perpendicular to each other.
The value of `hati(hatj + hatk)hatj * (hati + hatk) + hatk - (hati + hatj)` is-
If `veca.hati = veca.(hati + hatj) = veca.(hati + hatj + hatk)` = 1, then `veca` is ______.
If the two vectors `3hati + αhatj + hatk` and `2hati - hatj + 8hatk` are perpendicular to each other, then find the value of α.
