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`.
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`
Show that the vectors `veca, vecb` are coplanar if `veca+vecb, vecb+vecc ` are coplanar.
Find \[\vec{a} \cdot \vec{b}\] when
\[\vec{a} =\hat{i} - 2\hat{j} + \hat{k}\text{ and } \vec{b} = 4 \hat{i} - 4\hat{j} + 7 \hat{k}\]
Find \[\vec{a} \cdot \vec{b}\] when
\[\vec{a} = \hat{j} + 2 \hat{k} \text{ and } \vec{b} = 2 \hat{i} + \hat{k}\]
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
\[\vec{a} = \lambda \hat{i} + 2\hat{j} + \hat{k} \text{ and } \vec{b} = 5\hat{i} - 9 \hat{j} + 2\hat{k}\]
For what value of λ are the vectors \[\vec{a} \text{ and } \vec{b}\] perpendicular to each other if
\[\vec{a} = \lambda \hat{i} + 3 \hat{j} + 2 \hat{k}\text { and } \vec{b} = \hat{i} - \hat{j} + 3 \hat{k}\]
For any two vectors \[\vec{a} \text{ and } \vec{b}\] write when \[\left| \vec{a} + \vec{b} \right| = \left| \vec{a} \right| + \left| \vec{b} \right|\] holds.
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 \[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 5 \text{ and } \vec{a} . \vec{b} = 2, \text{ find } \left| \vec{a} - \vec{b} \right| .\]
If \[\vec{a} = \hat{i} - \hat{j} \text{ and } \vec{b} = - \hat{j} + \hat{k} ,\] find the projection of \[\vec{a} \text{ on } \vec{b}\]
Write the component of \[\vec{b}\] along \[\vec{a}\]
Write the value of \[\left( \vec{a} . \hat{i} \right) \hat{i} + \left( \vec{a} . \hat{j} \right) \hat{j} + \left( \vec{a} . \hat{k} \right) \hat{k} ,\] where \[\vec{a}\] is any vector.
Find the value of θ ∈(0, π/2) for which vectors \[\vec{a} = \left( \sin \theta \right) \hat{i} + \left( \cos \theta \right) \hat{j} \text{ and } \vec{b} = \hat{i} - \sqrt{3} \hat{j} + 2 \hat{k}\] are perpendicular.
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 \[\vec{a} \text{ on } \vec{b} \text{ if } \vec{a} \cdot \vec{b} = 8 \text{ and } \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k} .\]
If \[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 3 \text{ and } \vec{a} \cdot \vec{b} = 3,\] find the projection of \[\vec{b} \text{ on } \vec{a}\]
Write the angle between two vectors \[\vec{a} \text{ and } \vec{b}\] with magnitudes \[\sqrt{3}\] and 2 respectively if \[\vec{a} \cdot \vec{b} = \sqrt{6} .\]
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 \[\vec{b} + \vec{c} \text{ on } \vec{a} \text{ when } \vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k} , \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} \text{ and } \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .\]
If \[\vec{a}\] and \[\vec{b}\] are perpendicular vectors, \[\left| \vec{a} + \vec{b} \right| = 13\] and \[\left| \vec{a} \right| = 5\] find the value of \[\left| \vec{b} \right|\]
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 \[\vec{a}\] and \[\vec{b}\] are unit vectors, then find the angle between \[\vec{a}\] and \[\vec{b}\] given that \[\left( \sqrt{3} \vec{a} - \vec{b} \right)\] is a unit vector.
The vectors `vec"a" = 3hat"i" - 2hat"j" + 2hat"k"` and `vec"b" = -hat"i" - 2hat"k"` are the adjacent sides of a parallelogram. The acute angle between its diagonals is ______.
Let `veca, vecb, vecc` be three vectors of magnitudes 3, 4 and 5 respectively. If each one is petpendicular to the sum of the other two vectors, then `|veca + vecb + vecc|` =
The value of `hati(hatj + hatk)hatj * (hati + hatk) + hatk - (hati + hatj)` is-
If `θ` be the angle between any two vectors `veca` and `vecb`, then `|veca * vecb| = |veca xx vecb|`, when `θ` is equal to
